Detective it looks like you've fallen for the nonsense spouted about feminists by TRAs. They lie about what gender-critical means and what feminists think about trans people, to make it sound like it's all about hate, intolerance and some kind of conservative adherence to stereotypes.
No. GC feminists understand that trans people exist - ie people who want to think of themselves as the opposite sex and "live as" the opposite sex (though that is only possible by following sexist stereotypes) – but they do not think these trans people have changed sex. (Nor do many trans people themselves, of course.) And they think this matters, particularly for women, who are at risk from men as a sex class in various situations and suffer from unfairness because of their sex. Denying and ovverriding sex as a category endangers females, but not males - because of the inherent importance of sex.
We absolutely do not think you have to stick to some strictly defined gender stereotype because of the sex you were born and are. What bollocks. It's the total opposite. You have a sex, and because that can't change, it matters - for safety, privacy, fairness in sport, health and medicine, the disadvantages incurred by childbearing, who you're attracted to, and so on.
Aside from that, you should not be held back by your sex or limited by gender stereotypes about how you should look, dress, your interests, your sexual orientation etc. Feminists are opposed to gender stereotypes being forced on people because of their sex. That's what "gender-critical" means.
It is genderists who link stereotypes to sex by insisting that if you're a feminine man, you must be a woman, and vice versa, or thinking that a man can "be" a woman by adopting a bunch of offensive sexualised stereotypes that most women do not embrace.
Lastly, gender-critical feminists are, amazingly, not generally far right fascists. They tend to be lefties and often lesbians. Fascism and far-right movements aren't known for their defence of women's rights.
Some on the right agree with us, but that's because most people agree there are two sexes and humans can't change sex. It's just that only those on the right can say it without being massively persecuted by their peers because the left has swallowed all this guff.