society telling you that women are X when you, a woman, see yourself differently is going to feel uncomfortable. This is similar discomfort to society telling you that you're gender X when you see yourself differently.
The genderist view "I don't fit the gender society tells me I am. I must be a different gender. I need to change my gender."
The feminist view "I don't fit what society tells me a woman is. Society must be wrong about what women are. I need to change society"
And since gender is mutable and sex is not, both reactions are rational within their context (although I would argue that the genderist would ultimately be happier realising that gender doesn't even need to exist in the first place).
And the two can coexist quite happily as long as we recognise that sex and gender are two different things, understand when we are dealing with one and when we are dealing with the other, and don't try and use the same bloody names for them!
Someone who is okay with rigid societal gendered expectations of women would normally be called traditional, conservative, rightwing, or simply sexist. It's not related to their gender identity.
Depends on how you are using the word "woman" here.
Someone who is okay with rigid societal gendered expectations of female people would normally be called traditional, conservative, rightwing, or simply sexist - true
But
Someone who is okay with rigid societal gendered expectations of women based on gender as an identity which is inclusive of trans women - for example that idea that cis- and trans- women are just innately more feminine, caring, unaggressive sexually or whatever - would currently be called progressive and left wing!
So you see why trying to use the same name for completely different things can get us into a pickle of confusion very quickly. Which is a bad thing, unless of course one is deliberately trying to obscure what's going on.