What does "be it" mean in this passage?

As tchrist has mentioned in his answer, "be it" is an inversion of the present subjunctive of verb to be in a condition clause. This use is generally archaic, except for some instances where the meaning of the clause is "no matter whether ... or ..." such as posted in your question. Wikipédia

Examples

• "Be he alive or be he dead..."

• "Be it a genuine Renoir or not, I find this painting fascinating." (Whether it is a genuine...)

• International differences in the endowments with environmental resources do exist, be it because of differences in physical characteristics of the countries, be it due to differences in the tastes of the people" The Economics of International Trade

Your paragraph means "We are all influenced, to some degree, by the elements of culture of our homeland. Visiting another country will certainly show us different habits, some of them distasteful. It can be a different way of treating relatives, or simply a food we cannot manage to get down with a smile.

This is a use of an old way of phrasing things called a concessive subjunctive clause, as explained in this answer. You can tell because of the inversion of subject and verb and the switch from a present-tense verb form.

These days you are most likely to see concessive subjunctive clauses in fossilized phrases like this:

1. Come hell or high water, I’m still not budging an inch.

It means the same thing as this does:

2. Even if hell or high water should show up, I am still not going anywhere.

So in your examples, it’s just like saying that:

Even if it should be practices, a way of treating relatives, or simply a food that they cannot manage to get down with a smile, one way or another people will always find something distasteful in another culture.

CGEL 1985 says of concessive clauses:

Concessive clauses indicate that the situation in the matrix clause is contrary to expectation in the light of what is said in the concessive clause.

In olden times, clauses contrary to expectation took a different verb form than the normal one. Most such uses today are of a somewhat “elevated” register, be that one of literature or poetry, or sometimes of oratory or legal regulation. The previous sentence is an example of this, using a subjunctive construction under inversion.

But you don’t have to do it that way. Concessive clauses often start off with subordinating conjunctions like though, although, even though, even if, whether, no matter, unless, lest, or any of the various wh- + ever words like whatever, whichever, however, whoever, wherever, and all the rest of that ilk.

As one might guess from the occurrence of unless and even if in that list, they can be thought of as serving as the protasis — meaning the “if” part — of a conditional. The big difference is that they are assuming the negative of the verb they are governing, something “contrary to expectation”.

As such, concessive clauses historically took the subjunctive form of the verb, not the normal one. You see this frequently enough in the Early Middle English of Shakespeare and the King James Version. For example, Job 13:15 reads:

Though he slay me, yet will I trust in him.

Notice that’s “he slay” in the subjunctive, not “he slays” in the indicative. In casual conversation today, we would be much more apt to either put that in the indicative or use a modal auxiliary. For example:

3. Even if he should slay me, yet will I trust in him.

4. Even if he slays me, I will still trust in him.

The old conjunction lest still takes a subjunctive or modal:

5. Lest there were any doubt left, the plaintive showed the jury the brutal scars scoring and crisscrossing his back.

6. Lest there be any doubt left, the plaintive will show the jury the brutal scars scoring and crisscrossing his back.

7. Lest there should be any doubt left, the plaintive will show the jury the brutal scars scoring and crisscrossing his back.

Another way of forming an English conditional is to skip the conjunction altogether, but employ inversion and either a subjunctive or modal:

8. Were it otherwise, you would learn of this immediately.

Which just means:

9. If it were otherwise, you would learn of this immediately.

So you get inverted versions in the present, too, when making such concessions:

10. Be it for good or for ill, I will have it no other way.

11. Should it be for good or for ill, I will have it no other way.

If you use a conjunction, you don’t need any inversion, but the old-style way can still take a subjunctive:

12. Whether it be for good or for ill, I will have it no other way.

However, by using an explicit concessive conjunction, we can get it back to a normal present tense formulation:

13. No matter whether it’s for good or for ill, I won’t have it any other way.

14. Even if it’s for ill, I’ll have it no other way.

Most of the inverted subjunctives of concessive clauses today occur in fossilized phrases and are no longer productive. You don’t often hear people today talk like this any longer:

15. I will always be there for you, come what may.

16. Say what he will, I shall never believe him.

It would be more casual and less poetic to instead say:

17. No matter what happens, I’ll always be there for you.

18. No matter what he says, I’ll never believe him.

Returning at last to your original quotation, it could also have been worded this way instead:

People will always find some aspect of another culture distasteful, no matter whether it is customs and practices, a way of treating or relatives, or simply a food that they cannot manage to get down with a smile.

These really all mean the same thing. It just sounds a bit more high-falutin’ to use the “be it” version of the concessive subjunctive clause that your original has in it.