My gf is a huge feminist activist but demands I treat her like a sub in private and she is getting fat

i am a high IQ individual who works in data and i have been dating this girl for six months. publicly she is a major feminist activist who constantly posts online about the patriarchy and how much she hates men. she recently went to a protest about the new midterm voting laws. the problem is when we are alone in my apartment she acts completely different. she will text me things like "women need to be physically attractive and submit to men". she begs me to be aggressive and dominant with her. i have watched a lot of adult content in my life so i know what dominant behavior is but my social skills are poor and i just feel awkward doing it. i try my best to fulfill her requests because i believe people should strive to be physically fit and attractive and i want a good relationship.

the main issue right now is her weight. she has gained probably thirty pounds in the last two months. i view obesity as a personal failure becuase it shows a lack of self control. i brought this up to her in a very calm and logical way. i told her that her weight gain is making me less physically attracted to her and that she needs to fix it. she started yelling at me. she called me a misogynist and said i am influenced by bad media. then an hour later she sent me a message saying she wants me to punish her for eating too much.

i have no idea what to do here. i do not understand how someone can talk about hating men all day and then demand male dominance at night. there is this weird guy at her workplace who wears animal ears all the time and he told me i need to respect her public identity. there is also this total meathead at my gym who told me "you should just grab her and force her to obey". i do not want to grab anyone. i just want her to lose the weight and act the same way in private as she does in public. i am starting to think her brain does not work right. what do i do here.