First contact gave me the impression the human race were too busy blowing each other to bits, that race became irrelevant. I don't think anything was swept under the rug, there was no rug. According to the movie mankind solves poverty and other negative isms within 40 years or did they say 60? That means the chlidren born during or after First contact got their act together a lot quicker and better than their parents and grand parents did.
I suppose knowing aliens are out there scared the shit out of em. Racism/Prejudice was transferred to aliens rather than ones fellow human being if you follow ST ENT. Not so much enlightenment of humanity more 'lets pick on someone else instead' as showcased in TOS with Dr McCoy (IMO).
To be fair to McCoy, though I definitely think there are many times a line is crossed, I always felt his Anti-Vulcan stance with Spock was more akin to the friendly rivalries you get between ethnic groups, or cultural groups, or even individuals, that display what seems like something more similar than it is.....the kind of thing that happens between actual people as opposed to nebulous groups (two working class men in Britain might rag on each other for being southern, northern, cockney, geordie, English, Welsh Or scots....and to an outside observer it might seem like racism, but in the context of those people, that group, it is decidedly not, and is meted out in a balanced manner...there is no victim. As we see with Spock and McCoy barring each other. That kind of balance is often forgotten these days, and the barbs are treated as 'real' when not, or the barbs that are real are hidden under other excuses. A joke of that nature after all, is only funny when both sides can laugh at it, each other, and themselves. The best recent example I saw was what I assume from his profile was a Black British person commenting on a news story about Dune...and I paraphrase 'obviously Muad'Dib was Caucasian, they said he walked naturally without rhythm' . It's funny, but only if you know the racial stereotype to both groups is not meant with malice. Someone somewhere probably didn't find it funny mind you. Any real world inequality shouldn't come to bear on that joke, because basically, it's Dune fans talking about Dune. Sometimes I miss shows like The Real McCoy, or Goodness Gracious Me...the world is a poorer place without sensible humour lancing these things and showing them up. All of us, laughing at us, recognising difference but all the same...no us and them.)