I could make similar argument about a lot of things we do here, e.g., people hear "consequentialism" and think "the ends justify the means", that doesn't stop LW from promoting consequentialism.

Nope, and some people will express disapproval of LWers who promote consequentialism. Being right doesn't make you immune to social stigma.

Intentionally believing false things always carries a cost.

Yes, it does. So does unintentionally believing false things. This is definitely not a one-sided issue, as much as people like to pretend that is it. Anti-discrimination policies reduce one cost at the expense of raising another.

For example, suppose I want to hire the best mathematicians for a project, they'll likely be disproportionately White or Asian men.

In the case that you both want to hire and are able to hire exceptional mathematicians, anti-discrimination policies are likely to hurt both parties involved. (In theory, laws regarding disparate impact wouldn't actually affect you if you were hiring based on demonstrable mathematical prowess, but in practice business necessity would be hard to prove). The mathematicians are actually likely to be hurt considerably more, because without anti-discrimination policies, they would probably be in higher demand and thus able to ask for much higher pay.

The real problem comes in when employers decide that they need exceptional people but can't actually identify these exceptional people. If filtering based on race was allowed, employers would use that (the best mathematicians are disproportionately white and asian, therefore if I hire a white or asian I'll get an above-average mathematician).

Basically, you're right except for the problem where humans mix up p(a|b) and p(b|a), which causes people to do stupid things (most of the people who win the lottery buy lots of tickets, so if I buy lots of tickets I'm likely to win the lottery). If you actually know what you're hiring based on, anti-discrimination policies will prevent you from having 100% of your workforce be the very best, but even if only whites and asians had the required skills, you're still looking at 77% of the population in the US, so it falls in the category of "annoyance" not "business killer". In terms of fudging, you can detect statistically significant deviations just as well as someone looking at your hiring data. You don't need to know beforehand.

Of course, if these things weren't the case you'd still face social stigma for saying anything that sounds vaguely racist. Because while these two societal tendencies have strong effects in opposite directions, they're not there by virtue of reasoned argument, and so removing one but not the other is likely to cause more harm than good (probably, I have no idea how one would go about removing either societal tendency to test that hypothesis). If both tendencies could be eliminated, that would be best, and here you probably can talk about it without much social stigma, but if you ask those questions in everyday life, you will be labeled as a racist.