I'm simply saying there is no way to act like a man or a woman.

Sure there is. Go to a truck stop or a barber shop. Male stereotypes on the hoof. The same goes for women.

This is how drag queens work. They exaggerate female appearance and mannerisms.

Tons of trans people, if you actually engaged with the community, you'd realize, do not want cis approval.

They don't merely want approval -- they want acceptance as the genuine article. That's why there's the issue with changing birth certificates. They want the transformation made official. What makes you a girl more officially than a government document?

That spectrum sure seems to change to hard binary given the right conditions.