If what you say about gender “is the state of being a sex” is true, then explain why there’s alternate and derogatory terms for a boy who likes ballet and princesses; likewise with a girl who’s into football and cars. You’re using the same tired tautology.
“ If their state of being is as a female an OBGYN would apply.” Do you mean if the trans woman has a vagina? Because yeah, then they would be treated by an OBGYN. Just as how a trans man who has a vagina would also be treated by an OBGYN. What exactly is your point?
We’re talking about gender and sex. Stay on topic.