Let me discuss the details of your argument, as those details are very important. I will present a perspective of how gender critical trans activism might look like and later compare it with your perspective.
From my perspective a gender critical trans activist must make a clear distinction between sex determination systems, sex, different primary and secondary sexual characteristics and different aspects of gender which I gonna list in the next tweet.
Gender consists of (maybe among other things) the expectations and social pressure related to certain behaviours which form a system. That rigid system is considered oppressive by the gender critical movement, mostly towards women.
Some other aspects are the way people present themselves e.g. clothes, make-up etc. And yet another aspect is how people are perceived and categorized by the society (the problem of "passing" for trans people).
For trans activism an important aspect is gender identity. Gender identity can be understood in different ways and the issue of gender dysphoria also comes into play here.
Those aspects must be considered separately. A gender critical trans activist cannot conflate and confuse those issue for the sake of argument. Postmodernist "tricks" are not something a gender critical trans activist accepts.
Instead a gender critical trans activist accepts science including biology.
At minimum, a gender critical trans activist acknowledges an importance of sex as different from both sexual characteristics and different aspects of gender.
A gender critical activist accepts that sex is binary as well as a limited number of sexual characteristics, but some other sexual characteristics are discreete and some other are on a spectrum.
From this starting point a gender critical trans activist can make arguments against the binary of the gender system (but acknowledges the binary of sex).
Both gender critical feminists and trans activists can subscribe to rejecting gender stereotypes. Trans people often go above simply rejecting them - they also modify their bodies.
Claims about female "identity" are much less important in gender critical feminism than female sex and female-typical sex characteristics. The focus on identity is what derailed trans activism.
Instead, the focus should be on trans people bodies on one hand, which are atypical for their sex and on the other hand on trans people acting against stereotypical behaviours of their sex. Those two aspects should be the core of trans activism.
As you can see from my comments above, I think you should focus on the distinction between "female" vs. "female-identified". This disctinction is very important in the gender critical movement.
Trans activism of the future should move from the "identity" perspective to the rights perspective. Trans people do not have the right to female spaces unless they're female.
But trans people do have the right to modify their bodies (as adults) and they do have the right to reject social gender in any way. They do have the right to their own beliefs, but they do not have the right to impose those beliefs on others.
Some quotes from that article. Make your own opinion.
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"(white) cis women’s ability to claim a position of vulnerability in this context is, itself, a reflection of the power that (white) cis women have over trans women (as well as racialised subjects of all genders)"
What is bad is often not the things themselves but pressure to do them and consequences when one doesn't.
E.g. things like make-up. Without gender expectations it could be an interesting hobby or a funny thing to do from time to time.
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Just like any other hobbys. But it's something totally different when there is pressure in the society for females to apply it (it takes a lot of time which can be spent elsewhere) and there are negative consequences, if they don't.
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Things are often neutral (but some are not e.g. extremely high heels are unhealthy), but it's society values that makes them tools of oppression. Societies can make many neutral things into tools of opression.