What hairdresser does she go to that asks if she's male, female, trans or gay? They might ask general pleasantries so as not to awkward, but I have never heard one ask personal questions about sexuality before cutting hair.
She's so close to getting it when she notes that females always pay more, and also when she explains that she feels like an intruder in a barbers because of her female biology, but is far too desperate to insist that practically everyone else is completely happy with gendered expectations and it's only the very special trans/non binary people that suffer so acutely.