Was considering black-skinned people inferior to white-skinned people purely rational? It was well above the noise level for centuries. I don't even touch religious practices here. Find out why Daniel Kaneman received his Nobel prize.
OTOH preferring a job that pays $100k to a job that pays $50k would take a lot of irrationality. I suspect that most women are not that irrational at all, so there must be something very unpleasant that prevents them from landing these jobs in a reasonably equal proportion with men.
This is a broader question... is racism and other discrimination a rational act, or not? We need to be sure to not conflate individual behavior and group behavior here.
Now, as a group behavior, discrimination is rational. If my side is strong, oppressing the other side keeps my side strong and makes it stronger, and then weakens the other side. The moral dilemmas can then be rationalized away with fancy words.
As an individual member of a group that practices discrimination, it's also rational. I can go along with my peers, accept the fancy words even though I realize they're probably nonsense, and benefit from the superior strength of my side. Or, I can call out the immorality and nonsense, and get shunned and locked out of the benefits of my position.
Once you take morality out of it, discrimination is rational behavior. Making up ridiculous lies to justify discrimination is rational behavior. It's one thing to not believe it, another thing to act against it.
OTOH preferring a job that pays $100k to a job that pays $50k would take a lot of irrationality. I suspect that most women are not that irrational at all, so there must be something very unpleasant that prevents them from landing these jobs in a reasonably equal proportion with men.