Q1. What purpose does a Gender Studies Department serve.
Q2. Why are its teachings based not on science, but apparently on the opposite?
2) It's not based on the opposite. It's based on a superset of factors of which science is just one. We don't interact with other people according to purely scientific algorithms and so dealing with the emotional, political and philosophical aspects are equally as important as the scientific.
If the scientific process does not apply to Gender Studies, that's fine I suppose, it can be considered part of the arts. However, it would be an error to then consider forming policy based on it - similar to forming policy based on music or painting.
In order for us to make policy decisions or recommendations, there needs to be academic rigor, otherwise we may as well be a theocracy.
I know you didn't directly bring up anything about forming policy, so those points aren't necessarily directed at you. I bring them up because I see a lot of material from the field of Gender Studies being used to form policy, law and social expectations.
https://www.aaas.org/programs/dialogue-science-ethics-and-re...