Ahh yess a QT who responded! I recognize your username from some threads I've combed through. You seem to have gotten in some scruffles with the GCs here, lol. Well anyways, thanks for your comment, I think I have a few things to follow-up on: (I apologize for the shitty formatting ahead, I have no idea how to do quotations on saidit lol).

"All feminists, even feminists who are trans women, are fighting for women's rights" -Debatable, and depends on what the feminist's definition of "rights" for women are. Is it female liberation? Is it separatism? Is it gender abolition? Is it post-genderism? And what are the methods used, and to what end? For example, many 3rd wavers are supportive of the legalization and normalization of sex work. 2nd wavers would say prostitution and pornography are a stronghold of the patriarchy. There is a fundamental disagreement in ideology there, and it is impossible for them both to be right simultaneously. Only one of them is actually fighting for women's rights.

"Fighting for equal pay" -The problem is that before transition, trans women are treated as male and actually benefit from the pay disparity in the workplace, not suffer from it. I do wonder if there have been any studies done on transitioned/passing trans women in the workplace and what the paygap is compared to cis women, that would be interesting to see.

"to be seen as competent equals" -This is vague and subject to individual interpretation. What does that concretely look like, and what material objective can be pursued to achieve it? I've had conservative women tell me they feel most "equal" when they are subservient to their traditional husbands.

"being allowed to enter traditionally male professions" -Once again, this is something that pre-transition trans women benefit from, not suffer from. I concede passing trans women may face discrimination in this regard too though. I think some studies would be beneficial here.

"ending sexual harassment" -Yes, sexual harassment is an overlapping issue for cis and trans women. However, by ending sex-segregated spaces, you are introducing legal loopholes which would allow any man to identify into those spaces, regardless of whether that identity is authentic or not. Furthermore, given that 99% of men have penises and the sexual assault and harassment statistics against cis women and girls at the hands of men, cis women and girls have a right to not want to be exposed to these genitals in bathrooms and lockerooms.

"prosecuting rape" -Prosecuting rape is not just a feminist issue because it affects everyone. However, I'm glad you brought up the topic of rape, because it disproportionately affects females by male perpetrators. And by ending sex-segregated spaces, there are loopholes which will allow predators to enter those spaces unquestioned. This is already becoming an problem with female prisons.

"ending sex shaming" -I'm not sure what you mean by this. Are you referring to "slut shaming" or something else?

"a lot of feminists are fighting for OTC birth control and to end pregnancy discrimination" -This is great, these are important women's issues. However, abortion access and menstrual stigma are still priority too, ESPECIALLY in countries and cultures outside of the West. I have never seen trans women step up to the plate and fight with cis women to maintain these rights. Cis women are expected to fight for trans-specific issues, but trans women don't extend the same courtesy. In fact, it seems when they do talk about it, it's to say "stop calling them women's issues! you're making us feel left out" and center their feelings instead. At protests and marches for reproductive rights, pussy hats and uterus signs are branded as "TERF". Why are cis women not allowed to talk about issues that affect their biology and 99% of women in general? If it affects 99% of women, it's a women's issue.

"Title IX prohibits sex discrimination in education programs and activities... does not mandate nor prohibit sex-segregated spaces" -You're right, and this is my point. Title IX allowed for the establishment of sex-segregated spaces in schools and girls to be given their own sports etc. away from boys, by prohibiting sex discrimination. Prohibiting sex discrimination is what allows for girls to participate in opportunities that are equally afforded to boys. It applies to trans people too, you're correct, because trans people also have a sex. Furthermore, I am glad you highlighted that it was on the "basis of sex". Trans activists/feminists are deliberately trying to undo "on the basis of sex" by obfuscating sex and gender identity and render it meaningless. As I stated in my original post, if anyone can identify into any gender or sex, then there is no reason to have any segregated spaces at all based on either gender OR sex. Who would that benefit? girls or boys? men or women? Which leads me back to my original question. Why were sex-segregated fought for in the first place, why was it necessary, why was it an achievement for women's rights? It is these questions that no QT has answered me, as I said in the OP, which is why I have a fundamental problem with their reasoning.