Which leaves the question of which is the dominant effect. But for that anecdotes are useless, because "I've seen this happen myself" doesn't tell you if it explains 5% of the difference or 95% and people have a tendency of jumping to conclusions without having all the information. If Alice made bigger sales to fewer customers and Bob made smaller sales to more customers and Alice is white and Bob is black, then if Alice gets the promotion the boss is a racist because Bob made more sales but if Bob gets the promotion the boss is a sexist because Alice made bigger sales. Or so you would think by only listening to the one complaining about not getting the promotion.
So then you'd want someone to do a study and we're back to anyone publishing a study that challenges the prevailing dogma getting punished for it.
Statistically, white people make more money than black people and men make more money than women and there are differences in their proportions in various occupations. This could be caused by cultural differences that correlate with race, or hormonal differences that cause behavioral differences and correlate with sex, or it could be caused by racism and sexism. Much of the left takes it as an effectively religious position that the latter predominates even into present day. Many of them are quite militant and aggressive about it, and in particular will try to ruin anyone who presents evidence to the contrary or who opposes policies that would actively perpetrate injustice if their sacred assumptions weren't true anymore. Which isn't consistent with "live and let live".
And that's the nature of politics. You're never passing a law by a margin of 53 to 47 because everybody agrees with it. That's the 53% telling the 47% how to live.
"Only the other side does this" is false purity. There are no saints in Washington.