Well established: a woman is an adult human female. Try a dictionary, biology textbook, etc. You might not like it, but you can’t reasonably say that it’s not well established. I hope you agree that a “transgender woman”, or, to use more neutral language, a trans identified man, is not female. That’s the entire issue here.

Reasonable: see the above. Also, implied by the users of the term itself. If a T.W. is a W., why do they say T.W.?