I'm going to try to steel-man a trans-favorable position regarding aping a stereotype.
First, we stipulate that males and females are different beyond anatomy. This includes psychological differences. We are not blank slates with regard to sex, even psychologically.
Some/most/?? trans people have some significant aspect of the opposite sex within their psychology because they were born that way, because they are not just a blank slate.
But they also live within a society and culture with sex stereotypes. They perceive/filter/express their trans-ness through the lens of social sex stereotypes. There is some sort of interplay between the trans nature and the social reality they find themselves in that does not deny either.
I'd encourage everyone to first improve this steel-manning, followed by critique.
I like where you're coming from... but I confess that I don't think I can do it. I'll try to give it some thought.
I end up hung up because there are secondary ramifications to the assumptions underlying your steel man position.
First off, I concede that there are behavioral tendencies that differ by sex. I don't think this is necessarily a stipulation, I think it's a reality. We know there are behavioral differences by sex among most species, and that those behaviors tend to be more differentiated among species that have higher degrees of physical dimorphism. At a minimum, there are behaviors that are associated with the necessary differences of gestation and care of offspring.
Where I end up circling and unable to progress is that your steel man requires not just that those differences exist as tendencies, but that they be
prescriptive in nature.
For example... males tend to be more aggressive than females. Males tend to be more inclined to fight where females are more inclined to flight. This is generally true. But the next step that is unstated in your steel man is that if a male is more inclined to flight... that suggests that they're "less male" and "more female". It suggests that inclination toward flight means that they must be female in some fashion.
The result of that then ends up being that any male who is more inclined to flight than to fight must therefore be "female-ish", and not a "real man" - regardless of how they feel about it. Similarly, it would mean that any female who is more inclined toward fight must somehow be a male in terms of their behavior... whether they think of themselves as female or not.
What makes this even more challenging for me, is that it's all based on self-perception... and humans suck at this. It creates a situation where a male may
perceive themselves to be less aggressive than what they believe most males to be, and therefore their perception relative to other males means that they must be trans. But this subjectivity doesn't take into consideration whether they're within the standard deviation of aggression for females or not... nor whether females in general perceive them to be meaningfully less aggressive than males in general.
One of the things these past several years has shown me is that behavioral differences absolutely do exist, and that they're not all socialized learned behaviors. I've lost track of how many times I've observed a transgender identified male acting aggressively, demandingly, taking up a lot of space, being intimidating (even if unintentionally), and dominating the interaction... and all I can think is
"actual females don't behave that way". I'm far, far more confident and unabashedly in-charge than the average female is, I'm very much not a "stereotypical" female in terms of behavior... but the difference is striking to me.