Gonna get burried but OP, it seems like your sister may have wanted to use that as a means to socialize with you. It seems like that with her possibly identifying as a feminist with very... Open ideas about how a guy ought to be, it has caused her to tunnel vision badly. Simply put, you don't match up with her idea of a guy on her side, and that has caused her to flip out.

NTA. Atempt to explain both to your parents and her that it makes you uncomfortable and while you respect that other guys may be ok with it, this just doesn't match with your identity/preferences. That you're not her doll to play with. There is a chance you might not get through to her despite your efforts and that may cause a rift until she stops tunnel visioning. Best of luck.