>It is not in any way bigoted or transphobic to believe that a person being a man or a woman, and therefore the pronouns used to refer to that person, are determined by that person's sex at birth.

It is bigoted, because the implication behind this belief that all trans people are delusional, mentally ill or liars.

Mind you, I agree that "they" is an acceptable pronoun unless it's being exclusively used to avoid the chosen pronouns of trans people (in other words, it's fine to me if applied neutrally) and I think SO is going overboard here, but your comment has a lot of anti-trans bigotry in it you may not recognize.