Despite its guise of progressiveness, genderist ideology is - IMO - fundamentally and profoundly misogynistic and homophobic.
I don’t know if you share my views, but if you do, think how you would react if your DD came home and (inadvertently, out of ignorance) started repeating other reactionary, bigoted takes.
Would you agree with her and allow yourself to be “corrected” if she was coming out with something overtly misogynistic, like Andrew Tate’s ramblings?
I doubt it. So maybe think about how you’d address that, and see if any of it could translate over to this. I think it’s very important you find a way to explain to her that you’re not opposed to this kind of stuff out of ignorance or bigotry, as it is always made out to be, but because the ideas she’s parroting seem ignorant and bigoted to you.
You'd need to be able to talk about the impact of claiming some men are women or neither men nor women on women’s single sex spaces, how this whole ideology affects women’s rights, how sexist that is; also the whole idea of the cotton ceiling and how homophobic that is.
In age appropriate terms!
Don’t apologise or be defensive. You are not in the wrong here. She’s still very young and while she ultimately needs to find her own way on these issues, she absolutely still needs guidance, and she needs to hear your views in contrast to what others are telling her is the “right” way to think.