It sounds like your inner feminist is kind of judgy and self-righteous! I had one like that for a while, but I also was much less patient than you with the attitude that I should stop doing things I like and presenting myself the way I want to because THE PATRIARCHY also values those things. I didn't have inner dialogues like this, because I'd get about three sentences in and tell my feminist-self, screw you, if feminism is going to make ridiculous restrictions on my behaviour and self-expression and accuse me of false consciousness, I'll stick with sexism, thanks very much.

I did know that feminism is actually important, so in the end what I did was I imagined a new inner feminist for myself, modelled on feminists I like and admire (both public figures and my personal friends). That allowed me to have conversations with myself in which the defensive part, the wanting to look pretty and normal and have the life benefits that go with looking pretty and normal, felt supported and encouraged rather than attacked by the feminist part, the pointing out that it's really unfair that women have to look a certain way in order to get those benefits. And eventually my inner feminist voice kind of integrated into my outer self, so that I now call myself a feminist and go around stating overtly feminist opinions outside my own head.