Send colonists that aren't easily split into an "us" and a "them" group. Sending a completely homogenous group may not be possible, but how about the opposite: sending a completely mixed group? If everybody looks different, those differences also become meaningless. Try to send people from every country around the world. If you send multiple people from the same country, make sure they're from different ethnic groups in that country. Black, white and Native Americans, Han, Uygur and Tibetan Chinese, etc.

Part of the reason for racism, is unfamiliarity. You can see people as "Other" when we didn't grow up with them. They're a different social group. If you grow up with people who look just like you, and then you see people who look and act differently, that can create a very natural (but unjustified) sense of fear. If you want to prevent people from seeing different-looking people as Other, make sure they grow up with them, know them, and befriend them.

Also, maybe screen them before you send them. Make sure they're all educated enough to understand the destructiveness of prejudice.

The human race will barely start colonizing space until it switches its social policy to Communism. I doubt that capitalistic formation could ever arrange colonist missions because its too expensive and has below zero (even in distant perspective) chance to be profitable.

So if we take this as an assumption we may not worry about racism problem by the time of "Space Colonizing Era", because racism is a thing that has to be overcome already to achieve Communism, because Communism implies total equality of people with zero discrimination.

We might think of some kind of restoration of racism in distant future, when humanity faces aliens and needs to form relationships with alien race. And I suppose this challenge could be much more tough, but its another story.

I highly recommend you read The Moon Is a Harsh Mistress by Heinlein. He confronts this topic head on, with tribalism popping up overnight. He is so insightful when it comes to how humans and societies react to plausible tech. Despite his works being so dated, they are still highly relevant! Luna colonists quickly become seen as crazy "Loonies", while Loonies call em "Earthworms" and other derogatory slang.

I'm going to say this is impossible to accomplish. I'm going to point out the brown eyes/blue eyes "racism" study from the fifties.

https://www.youtube.com/watch?v=oGvoXeXCoUY

https://www.youtube.com/watch?v=1mcCLm_LwpE

https://www.youtube.com/watch?v=ebPoSMULI5U

https://www.youtube.com/watch?v=jPZEJHJPwIw

And the work done about empathy in this article: https://www.economist.com/open-future/2019/11/04/does-your-brain-care-about-other-people-it-depends

In all of these studies, arbitrary divisions of the people resulted in US vs THEM and in all of the cases, the participants were fewer than 100 people. And anyone seems to be able to introduce these issues simply by making an arbitrary division.

People that sleep on level4 vs level5 vs level6 would be practical and logical divisions during transit. People that live on the outskirts vs the center, People that live on the left side of the stream vs the right.

Phrases like "Wrong side of the track" were used to make people "them".

I think you are going to need continuous "team building" exercises to keep cliches from developing. Racial Cliches are the beginnings of Racism.

In my own personal opinion, I don't think we will face any type of discrimination among ourselves, as to colonize Space in our biological form would not only be futile but also a very bad idea and utter waste of human life. In my opinion, there will be a new type of discrimination and we will be the ones to be on the receiving end if we continue to act like the uncivilized creatures our destiny seems it wants us to be.

It is in my view that we are not alone, it's very likely that we are not and if we continue with our petty ways, the only ones to go to the stars will be the elite, rich and powerful. You know what? I think it is 100% fair that it should be as such. To allow an ordinary civilian into Space would only anger species a bit more intelligent than us. We will be wiped out in a flash. We will divert our discrimination and repeat our stupid mistakes and upset the wrong "people".

Extremely and highly intelligent beings more than likely create universes, giving them time to its limbo (That is our "God" or Higher Power, whatever you want to call it) - they will just allow mother nature to take its course, as we do in we play in our online virtual worlds, and no "God" will save us, as we will be the newcomers and not worth the effort. At that stage of our evolution, we will be at bottom of the food chain for the second time in our history. It's not wise to send a human being to colonize Space, as we are today. I guarantee we will mess it up and a handful of people will be responsible for the extinction of our species.

Only once we can live in harmony, be mindful of our peers will we have the maturity to deal with whatever Space may throw at us. Right now humans will only militarize Space, that the only thing we are capable of when we decide to do our little self-inflicted adventures of self-importance. We are nothing and exhibit absolutely no respect for love, life and we don't even believe in ourselves, now you want to send that into Space? We will get taken out so quickly, and 10,000 years of humanity will be destroyed in a split second. To me, we must have guidance from other species, we need to have advocacy from an ally to ensure our safety because our politics just won't be tolerated among more intelligent species. We are only safe (militarily) because we cannot get out of our solar system. It's that simple to me personally. To colonize space without an ally from another world or whatever will be the stupidest move, even the most intelligent, humble, and bold politician will make. You will have the "South Africa effect". All hunky-dory, until that leader is tired and dies. Then all will fall out the window. I can pretty much guarantee that humans refuse to learn from others better than themselves, purely because of jealousy, and their own human condition. For us to colonize Space outside our solar system without an ally we only lead to our demise.

Human history repeats itself, and right now we still can't learn from our own mistakes, even after like 3,000 years of constant war and suffering we still haven't learned. Why? We all want instant gratification and I doubt more intelligent species behave like the "children" we are. In fact, I hope they do everything in their power to stop us from our own stupidity and ignorance. Right now, humans won't even set foot on Mars in 80 years. We don't have what it takes in my own personal opinion, there are too few visionaries and too many self-imposed importance among our species. I find it rather sickening and I fear if we ever will have our future days of Star Trek Discovery. In fact, we don't deserve the privilege.

Racism will be forgotten and eradicated because we will be forced to futility defend ourselves against an imminent and humiliating defeat. I apologize for the passion in my writing, but I am tired of racism. I was born into it, and because of dumb humans, I will more than likely die from it. Human beings only disgust me, and we should truly feel ashamed of ourselves.

Psychologist David Eagleman described a story about Native American leader who was able to overcome tribalism (yet another variant on "us-vs-them" struggle) and to unite various tribes with following method:

"A leader named Deganawida forged peace by assigning each tribe member to one of nine different clans: Wolf, Bear, Turtle, Sandpiper, Deer, Beaver, Heron, Eagle or Eel. Thus, members of each clan had representation from all five tribes and crosscutting relationships now unified the community. By emphasising the overlapping dual allegiances—to tribe and to clan—Deganawida complicated the notions of us and them, defanging the intertribal warfare."

Source: https://www.economist.com/open-future/2019/11/04/does-your-brain-care-about-other-people-it-depends

In other words, he randomly assigned all tribes' members to artificial tribe-independent groups and thus every person suddendly identified with somebody from other tribes, based on this new group division. Therefore, the other tribes weren't just "them" anymore.

Make it Small, but Make it Fair

Racism isn't new. You'll never fully get away from it... unless you start small enough. Take no more than 100 people. As long as there's not a closet racist among them (and maybe even if there is, see what Daryl Davis managed https://www.npr.org/2017/08/20/544861933/how-one-man-convinced-200-ku-klux-klan-members-to-give-up-their-robes you won't start racist. Don't mind too much the racial or gender makeup of your colonists beyond what you need to secure good long-term genetics. Better to have a competent Hydroponics Specialist and no X Ethnicity than a bad one OF X ethnicity. If the only white/black/Maori on the colony is an incompetent, that's Not Great for racism.

Why 100 people? That has to do with Dunbar's Number https://en.wikipedia.org/wiki/Dunbar%27s_number which basically says a person can only know about 150 people "well". I went with 100 because 100 is the low end of his confidence level. Basically 100 people is a number that guarantees every person will know every other person well, and leaves room for initial colony growth.

So your 100 people start their new colony. It's too small a population for out-groups, especially if every group is vital for the survival or the rest. Sure you can look down your nose at the Cooks, but suddenly you and only you keeps getting shorted at mealtimes. Or given water that didn't QUITE recycle correctly and tastes vaguely of piss. Afterfew generations your colonists will probably be mixed-race as we would see it from Earth. But even before "Ethnic Martian" becomes a genetic thing, it'll become a psychological thing. Your people will suffer and triumph together in cramped conditions, and that breeds togetherness. For example, I went to Virginia Military Institute. The summer before new cadets start they have the chance to go to the school and take a summer class, no VMI Discipline. One of these new cadets, let's call him Tim, was a Good O'le boy in the best way.... except if you hung out with him a bit you quickly realized it was both racist and homophobic. Cut 2 months later, and the stress and hardship of the "Ratline" beat THAT out of him, and the gay black cadet is his best friend. The "Other" had become Citadel cadets, or the college kids at W&L. So too your colonists. Fast forward another 10 years and Tim had a gay black man as best man. Any prejudices against Ethnicity X will take a nosedive when Ethnicity X heads the Emergency Repressurization Unit or helps you out when your quota comes short or whatever. So long as you start off small enough that holding onto any earth-based ethnic biases aren't possible.

So keep it small and competent, and your colonists will become their own tribe. No intra-colonial racism, huzzah! That's great.... except inevitably there'll be another tribe. maybe it's the Wave 2 colonists who "just don't know" what it was like on Alpha Centauri when the micro-meteors hit. Maybe it'll be those idiot Terrans who weren't smart enough to be selected to colonize Mars and so are OBVIOUSLY Untermench. At the end of the day only another sentient species will really kick racism (and probably not even then). Even if you magically homogenized the ethnicity of everyone on earth you'd still have people from region X mocking region Y and vice-versa. If region X becomes more powerful than region Y then Y people will be oppressed and the whole thing starts all over again.

I think it depends less on the selection process and more on how the colony is run.

Strong leadership and discipline

With a strong leader and clear hierarchies enforcing discipline, no one will dare act without support from above. In a disciplined organisation such as an army, getting results is more important than petty class/race war, and the leader is interested in maintaining high human resources and therefore won't jump to racism themselves. Rationally, any human is potentially more good than they cost, regardless of race.

The ideal leader is a Machiavellian prince; "Machiavellian" not in the modern sense of the word (scheming, self-centered), but in the way Machiavelli described it: A leader who invest most of his power into staying in power and strengthening his position. The leader should be strong enough that none dare oppose them. When done well, this creates peace and stability as well as a focused push towards the objective, with any notion of internal conflict quickly extinguished by the leader in a show of strength.

Focus on an external threat

The only way to really unite humans is through an external threat. With all humans working towards the same goal, this external threat may be the scarcity of resources and the possibility of critical mission failure. Scarcity is dangerous as it can as well create a struggle over control of the resources, so we still need strong leadership to keep it under control as well as the assurance that no one is favoured in allocating scarce resources. Generally the leadership should run some propaganda to further highlight (and maybe exaggerate) these dangers and how important it is to stick together to overcome them.

Mandated selective reproduction and youth training

As a more extreme long-term measure, you can take strict control over reproduction: Select couples to mate based on genes but also such as to intermix any races and cultures that may still exist. Then take the babies from their parents and raise them exclusively in government controlled childcare and training centers. This way you can brainwash them towards supporting the existing leadership as well as teach them your own culture, thus ensuring everyone in the population follows the same culture.

Create a culturally and racially homogenous ethnostate.

I'm going to write a frame challenge answer, giving one solution that you deliberately excluded in the OP: the creation of an ethnostate by only allowing members of specific cultural and racial groups into any given colony.

After all, if there are no different racial groups within the colony, there wouldn't be any racial lines for racial discrimination to work along. White people can't oppress Black people if there are no Black people there to be oppressed, or White people there to do the oppressing.

However, if there are, then people will bring their pre-existing biases with them into the colony, and the fact of the matter is that there will always be winners and losers in any human society, and that power imbalance will always result in some degree of ethnic strife since it will never be perfectly balanced.

Indeed, this has antecedents in real life; the entire point of the subcategory of genocides referred to as "ethnic cleansings" is to create this state artificially by removing from a community members of other ethnic groups.

Have an alternative Scape Goat

As other have stated an "us" vs "them" mindset is inevitable in a larger population with varying degrees education and mental ability. Propaganda blaming a villainized Other is a necessity in a tightly controlled population. Just make up aliens or some faux domestic terrorist group (with some made up anti-social manifesto) and constantly run media stories blaming them for causing all the problems and diversity your civilization faces.

The added benefit is you can accuse anyone who threatens your power or leadership as being a part-of or working for the Other. Smugglers cutting in on your tax margins? No problem, they're treasonous secret agents plotting militia warfare.

Its kinda a non sequitur, but what else are you gonna do? Properly educate your entire populous? ...come on.

Alternatively simply remove it from the discussion, you can talk about racism, but don't put much weight on it. The cultural attitude is simply: it's a dumb idea for dumb people.

Let the population interbreed with-in a few generations every body is gonna be pretty genetically mixed up anyway.

In a colony where everyone has to band together just to survive the hardship of space, nobody got time to waste blaming skin color for their problems. The other is simply the harsh mistress of surviving space.

Historically, only one thing has ever put a dent in racism.

Freedom.

Among many other possible ciations, I offer just two classics. This is a theme repeated many times in Friedman's and Sowell's work.

https://www.amazon.com/Free-Choose-Statement-Milton-Friedman-ebook/dp/B004MYFLBS/ https://www.amazon.com/Economic-Facts-Fallacies-Thomas-Sowell-ebook/dp/B004THDT8A/

Consider that, in the 1920s, blacks in the USA were rapidly closing the gap with whites. They were rapidly becoming more educated. They were rapidly increasing their incomes and closing the gap. They were becoming professionals of all types. This continued until FDR's New Deal. Since then it has been a frustrating process. Advances have been slow and hard-won.

Consider a business with the goal of making money. Suppose two guys apply for a job, one of the racist-accepted group and one of the racist-hated group. If the business turns down the racist-hated guy, they decrease their talent pool, and so reduce their chance for profit. This punishes businesses that operate on racist principles. This process was rapidly bankrupting racists during the 1920s. When government stepped in, this process was largely squashed.

The government bodies of your space colony must stand as guardians only. They must keep people from using violence on each other. After that, people are free to do as they wish. In the absence of government support for such things, racism is quickly punished by the free market.

Racism is irrational. But: it is not obviously irrational.

At first glance, it works. As a kid, you are more likely to get beaten/bullied by other kids in a neighbourhood where kids are of different race/etnicity/religion. You get it before you understand words like race/etnicity/religion. You need to grow up a lot (and most people don't grow up that much at all) to see that this is self-fulfilling and has no substantial basis. But kid's experiences last forever.

Then, the politics kicks in. The distinction "us vs them" is pretty much important in politics, otherwise we don't need the politics. Here, racism and friends are cheap (short term) and powerful (short term).

So no escape from it. It can be managed (like substance abuse, gambling, etc...), but probably never eradicated.

Consider that most of what's called "racism" in the US today is really closer to culturalism. Then select your colonists from engineers and other technical types, who have their own subculture. (Just as NASA does with astronauts.)

If these are actual colonies, rather than just long-term bases, the original colonists will soon intermarry, and there will be no "race" to be racist about.

Impossible

My grandfather hated black people. Not a little bit. A lot. He was a racist. My father wasn't a racist, but was certainly biased. He's had excellent working relationships with people not like himself, but he also tends to use a phrase Grandpa used a lot whenever he hit his thumb with a hammer or encountered a difficult-to-solve problem. He'd call it a "cotton-picker." My siblings and I don't believe ourselves to be racist at all and we all have very productive relationships with people of all kinds of genders/identities, races, ethnicities, religions... (and consider the phrase "cotton-picker," and any phrase like it, to be abhorrent).

And yet I'd be an idiot not to recognize that I have basic biases. I obviously prefer to be around people who are a lot like me (especially if they tend to like my sense of humor).

I'm going to be blunt. Really blunt. I regret being blunt, but I'm neither apologetic nor repentant at all.

Everybody has biases and everybody's first reaction to having those biases pointed out is to blame something/someone else. Only an idiot would believe it's possible to eradicate biases.

As a younger man I used to think that all society had to do to completely resolve racism (and poverty, and a host of other social "diseases") was for humanity to mature a little bit. To "grow up."

I'm older now and though many (generally below the age of 40) will disagree, the reality is that bias (in its ugliest form, racism, or any other kind of "ism" that idiots will use to justify antagonism, hatred, violence, or even simple discrimination) is simply a part of life. It's why we have law — because without a framework to force us to behave differently, those biases tend to take over.

• 99.9% of us spend the first 12 years of our lives, arguably the most critical years when it comes to forming basic human relationships, looking at and living with people who look just like us, believe just like us, and act just like us (or, more accurately, we learn to act like them). The fact of families creates natural bias.

• 99.9% of us are fundamental creatures of habit. Even when we like change, most of us don't like the process of change. As a smoker, how hard it is to stop smoking? Now ask a white person above the age of 40 how comfortable they would be watching BET television? The problem isn't black actors (I'm a HUGE fan of a lot of black actors. Sidney Piotier, Morgan Freeman, Denzel Washington, Hallie Berry, Diahann Carroll, and Thandie Newton, to name a few), but the reality is that watching all-black television is uncomfortable — not because the stories aren't engaging or because I don't like black people, but because I'm simply not used to it. I, like everyone else, am a creature of habit.

And then, there's a fundamental truth expressed by a clever advertisement for the Sniper from the game Team Fortress 2:

'Cause at the end of the day, long as there's two people left on the planet, someone is gonna want someone dead.

The fundamental bases of all bias are anger, distrust, ambition, fear, and competition. You would need to eradicate all of those emotions/circumstances to eradicate racism.

But you must eradicate human nature to do it.

We all feel anger, distrust, ambition, fear, and are competitive, at many times during our lives. We aren't racist when we choose not to allow our reactions to these things to express themselves a hatred (in one form or another) toward someone else.

So, the reality is, if you stock your colony completely with 50% white 24-year-old women and 50% white 24-year-old men, all having the same political beliefs, religious beliefs, the same genetic background, the same cultural history, the same everything, then create training programs to minimize discrimination and law to prohibit it, you'd nevertheless have bias in a week and the very same hatreds, bigotry, biases, prejudices, and problems that we would today call "racism" within a year — if only because someone thinks your job is less valuable than theirs, or your eyes less pretty, or you're a centimeter shorter, or your nose a bit longer, or you tend to use the word "sanguine" too often....

In a word, it's impossible. To forgive may be very, very divine... but to have biases is human. A story that presented the utopic idea that racism had been eradicated would, IMO, have very low credibility because anyone reading it would (at least subconsciously) know that it's fake. You could minimize it, but never eradicate it.

Selection, training, and discipline

In the real world, space agencies are very careful to hire the right people. Astronauts are hired from elite fields, subjected to extensive psychological examinations, and trained for years. The slightest deviation from official policy can bring substantial consequences (just ask Apollo 7).

These strict policies would continue as the candidates for the colonization mission were selected. It may sound like an overwhelming task to find thousands of qualified candidates, but a country with the resources to send that many people to Mars can handle the vetting process. After all, the United States has approved more than 4 million people for security clearances. All of these people have been reviewed by federal authorities. People who pass the background check and who have the necessary skills would move on to psychological testing like what's used for astronauts. Then the training would start. The thousands of colonists would live together in a compound and train together, possibly for years. In that high pressure environment, racist tendencies would show themselves and anybody expressing racist tendencies could be cut from the program. By the time the team got to space, everybody would know each other and have experience accomplishing difficult tasks together.

The first wave doesn't get to have 'avoiding racism' as a criteria, at least, not in the way you've defined it. Avoiding people that are innately prejudiced is a good thing. However, requiring specific demographic representation is just a bad idea. The first wave of a colony, at least a first wave picked for maximum success, is a very carefully chosen group of people such that everyone can equally pull their own weight when it comes to everything that's needed for a space colony - scientists of every necessary discipline, doctors, engineers, astronauts, etc. Every person picked will need to fit a very select criteria, and adding an additional element to the criteria which doesn't affect the success/fail chance of the mission is a terrible idea. Or, to put it this way: Would you rather a colony without racism that doesn't work or a colony with minor racism that does? Of the two, only the later can be fixed - a failed colony will likely kill everyone there, and there's no cure for death.

Obviously, having racists in terms of the bona-fide variety of people who believe that people outside their specific demographic are inferior to them can't be tolerated, but that problem can be solved with a psychological evaluation, which will have a specific focus of seeing whether or not applicants can work with people from various demographics. If they can, great; if not, they're a liability.

The second wave, that is, people who come after the colony is established because the colony just needs workers to help sustain it and to have it grow bigger, can be given a bit more leeway when it comes to selecting the applicants from various demographics. If you so choose, you can limit the number of accepted applicants from every demographics such that it perfectly matches the percentages.

As pointed out by Dan W in the comments, making sure there's as much genetic variety is possible is a good idea to give the settlers the best chance against any potential threat that certain rare genes may provide.

However, even given that, strict racial quotas isn't necessarily a good idea, because you'll almost certainly be excluding more qualified applicants when your quotas are hit, so there's that. Also, you didn't mention it, but I'm going to point it out anyway - having children is a large part and parcel of developing colonies, so everyone who applies should do so on the understanding that they're going to be having children once they reach the colony.