Don't think it can't or won't happen.
We've already seen private organizations -- groups that should have the right to choose their membership -- successfully sued because they didn't admit women, gays, blacks, Mexicans, transgenders, nerds or whatever.
That was wrong.
For all this talk of "rights" where are mine? If I don't want to rent my house to a Mexican family I'm a bigot. If I don't want to hire lesbi-butch I'm a homophobe (despite the fact that I know my clients would shun me if I send lesbi-butch to call on them). If I want to go to a men's only golf club where I can get away from the wife and "be a guy" for a little while, well I can't do that either.
All of that is just plain wrong.
We started down this path of the government deciding what's best for people with the whole integration thing. Forcing a society that wouldn't exist when left to its own devices is wrong. Social engineering is and was a horrible idea. So is everything else that's followed.