For example, here is an informal writeup of a PNAS article finding evidence of bias favouring male over female job applicants when everything about the applications was exactly the same apart from the name.
That's not necessarily irrational in general. The other information on the resume does not prevent the name from also providing potentially relevant information.
I'd suggest you look up "screening off" in any text on Bayesian inference. The explanation on the wiki is not really the greatest.
But when you have information that is closer and more specific to the property you're trying to predict, you should expect to increasingly disregard information that is further from it. Even if your prior asserts that sex predicts competence, when you have more direct measures of competence of a particular candidate, they should screen off the less-direct one in your prior.
I remember seeing a talk of the concept of privilege show up in the discussion thread on contrarian views.
Some discussion got started from "Feminism is a good thing. Privilege is real."
This is an article that presents some of those ideas in a way that might be approachable for LW.
http://curt-rice.com/quotas-microaggression-and-meritocracy/
One of the ideas I take out of this is that these issues can be examined as the result of unconscious cognitive bias. IE sexism isn't the result of any conscious thought, but can be the result as a failure mode where we don't rationality correctly in these social situations.
Of course a broad view of these issues exist, and many people have different ways of looking at these issues, but I think it would be good to focus on the case presented in this article rather than your other associations.