I will quite happily use a transgender person's name and pronouns. I agree that sincere gender identities should be respected. However, it's also true that one cannot change one's birth sex. It's also true that our birth sex is a part of who we are.
I've heard it said that a transwoman is to a ciswoman what margarine is to butter - once we get past the superficial similarities, we see many fundamental differences. It's just plain lunacy to insist that someone born and raised as a boy, and went through puberty with a male body could possibly know what it's like to be a woman. The same is true for someone born and raised as a girl, who went through puberty with a female body, claiming to know what it's like to be a man. Transwomen are not women; they are men who live as women. The same is true for transmen; they are women who live as men. We must never lose sight of this. Activists like Magdalen Berns or Cathy Brennan get a lot of undeserved shit because they won't consider transwomen as sexual partners. Also, the depraved antics of Jonathan Yaniv and Stefonknee Wolscht aren't exactly helping trans* acceptance.
TL;DR - respect gender identities, yet never lose sight of biological reality.