A word like "engooden", for converting something from negative to positive

In your example the person isn't really changing something that was bad into something good, that is, changing something that pretty much everyone agrees is bad into something that everyone agrees is good. Like taking some piece of worthless junk and turning it into a work of art, turning a company that was going bankrupt into a profitable one, etc. Rather, he is changing, or trying to change, people's opinions about the thing.

If you still think the thing is bad, I believe the general term is "whitewash". For example, "Jones tried to whitewash his racist ideas by convincing everyone that it is good for the economy" or some such. But if you agree the thing is really good ... I don't know a single word for that idea. We normally use a phrase, like "convinced everyone this was really good" or "altered public perception" or "changed people's opinions", etc.

Note that "turned it on its head" could be used to describe this idea, but that phrase can refer to many kinds of reversals, not just bad to good. Like you could say, "Smith's use of the harpsichord in his rock concerts has turned the music world on its head ..." That doesn't imply that other instruments were bad in any moral or even artistic sense, just that he's radically changed things. Similarly for some other suggested phrases.

Transforming something considered bad into something that everyone considers good, might be described by adapting a well-known expression ("you can't make a silk purse out of a sow's ear") as:

Turning a sow's ear into a silk purse.

The example you give, however, sounds more like an attempt to turn something considered bad into something everyone considers good -- a different thing altogether.

Consider the following:

• Sublimate: transform (something) into a purer or idealized form
• Ennoble: lend greater dignity or nobility of character to
• Ethicize: to make ethical or endow with ethical qualities

Also consider terms like the following:
• spin, “To present, describe, or interpret, or to introduce a bias or slant so as to give something a favorable or advantageous appearance.”
• varnish, “To gloss over a defect”
• gild, “To adorn” (ie to apply a thin layer of gold, making something that's base appear valuable; also see aurify)
• transmute, “To change, transform or convert one thing to another, or from one state or form to another. [eg] The alchemists tried to transmute base metals to gold. ”
• transubstantiate, “to change into another substance : transmute [eg] The novelist transubstantiated the joys and sorrows of his early years into a charming fable about childhood”

Various social movements have reappropriated (or reclaimed) words and symbols that were terms of abuse into terms of pride in identity— queer and redneck of recent note, but also Quaker and Tar Heel going so far back that their original pejorative meaning is forgotten. Generally, however, reappropriation applies to labels rather than the underlying concept.

(A related concept is euphemization in which an inoffensive term is substituted for some concept to make it more socially acceptable to discuss. If the underlying concept remains somehow distasteful, of course, the euphemism becomes the new pejorative, a case of semantic change— or colloquially, the "euphemism treadmill").

Ideologies or identities may undergo a rehabilitation from time to time. To take an extreme example, David Duke attempted to rehabilitate the Ku Klux Klan's public image, replacing bombastic rhetoric with euphemisms like "racial realism" for white supremacism, dressing in a suit and tie instead of mask and robes, and staging press conferences instead of secret meetings. None of this "improved" or "reformed" the Klan in any meaningful way, but it did make it more accessible.

The original word or idea may also be exalted, elevated, ennobled, and so on short of full reappropriation or rehabilitation.

jwpat7 presents the best and most precise of extant possibilities with spin, I think (gild and whitewash are passable too, if a bit archaic) and I LOVE urbycoz's neologism positivise--a satirical gem worthy of Mencken! But considering the growing percentage of PR-types engaged in lipsticking various pigs, we need a good arsenal of synonyms: tart up, virtuefy...

Or if the transformations are real (excuse my doubts) there is the older verb uplift, which I note with some dismay is making a comeback. I'd prefer something like abracadabricize to indicate the magic process.

As @Jay has said, in the example the OP has been given xxx doesn't change anything about racism, he just gives an opinion of it. So despite what the OP has been asked for, the process is not of changing a thing from bad to good, but a process of presenting a view of something which conflicts with the popular, but not universal, opinion of it.

In that light I would suggest the verb 'To Recast', defined in the OED (Sign in required) as

To give (a person, occupation, etc.) a new or different role or image; to reinvent or re-present as something different.

I wouldn't advise using it for that particular case, but the word having the exact meaning you seek is

justify: to prove or show to be just, right, or reasonable - MW