> So is gender research or feminist queer dance theory studies a part of basic or applied science?
People's ideas about how humans should live together can be beneficial for the wealth and well-being of whole societies and its members. Was Rousseau part of basic or applied science?
We can wonder about how useful certain efforts are, of course, especially in all their extent; but I don't know how wise it is to dismiss things _wholesale_, just because their application is not immediately apparent and the rejection fits into the political current. The unnecessary snark is just sad to see here.
This one is easy - neither. The term "science" has gone through semantic dilution in a manner similar to how everyone is now an engineer - software engineer, prompt engineer, sanitation engineer.
Falsifiability is one of the key distinguishing characteristics of a proper science, as famously propounded by Karl Popper.
"Gender identities" not only can not be falsified, they should not be falsified, because that would amount to transphobia; denying the existence of someone's felt and lived gender identity is the definition of transphobia.
Since they cannot be falsified, nor even directly observed, measured, nor quantified, they are not scientific notions.
The closest most well-studied analogue to the "gender identity" is the legacy religious notion of "the soul," to which you will see you can ascribe most, if not all, of the same attributes as ascribed to the "gender identity."
Depends on the circumstance, surely? If someone is claiming a "felt and lived" identity to justify an action that infringes on the rights of others, is that not reason enough to deny it?
It depends, this could be medicine or it could be sociology or it could be psychology, there's a few different places it pops up.
> feminist queer dance theory studies
This is very obviously performing arts or maybe something in English or Social Studies if the "dance" part is the specialization rather than the core. I doubt even the most died-in-the-wool woke-fessor or whatever would call it "science," which makes it pretty irrelevant to the current conversation, though just because something isn't STEM doesn't mean it's not important (though it might be significantly less lucrative).