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),

Ironically this is a case where p(a|b) is in fact a good proxy for p(b|a) and and the kind of filtering you're objecting to is in fact the correct thing to do from a Bayesian perspective.