Rachel is an interesting character, as she's a bit of a stereotype right now. It wouldn't surprise me if it turns out she doesn't really know what she's talking about (as a reminder, she was against Math because she failed a math test: her ideology could be tied to lack of knowledge and awareness) and slowly turns herself around. Either way, she's begun to already see where she's wrong. I have complete faith that cosy can (continue to) knock it out of the park
I don't know if she is a stereotype per se. Definitely an amalgamation of several tropes. Pretend smartest person around? Check. Hero complex? Check. Annoying busy body? Check. Feminism as a crutch/excuse for behavior and making everything about gender? Check.
You see she pretends to be smart (Vicky and Lucy are smart), wants to save people, so she gets in a position of power (student body president or whatever its called), and uses feminism as a crutch to try to shut people down by "acting" smart and blaming everyone else, besides herself. Most people just don't want to deal with her so they let her do her thing. How do you deal with a narcissistic? Ignore them. This is what everyone with real intelligence has done in the school. The headmistress, the MC, etc. Ignore them and don't give them a platform.
What is interesting to me is to see how she breaks. Does she just become a nice little slave or is she going to be something more. I bet the later. Each girls personality is showing in how they are acting in the story.
Lucy = Mother of restaurant and home
Vicky = Slave who wants attention
Akatsuki = Catgirl
Sarah = ??? She is shy but feisty when she has courage .. who knows where this goes.
Hannah = ??? She is quiet and deliberate .. who knows where this goes.
Catherine = ??? Bold and Prideful .. who knows where this goes.
Allison = Confidant & advisor