But the fact that men should do something while women shouldn’t, or women should do something while men shouldn’t, to me it is sexist.
Define further please. Do you mean even if there is a good reason which makes sense?
For example, suppose there are separate bathrooms for men and women, does that bother you?
Suppose that girls in Orthodox communities have shidduch resumes because of the laws of supply and demand, but boys don’t, does that bother you?