I do not reveal my medical history to people I date, especially if it is the early stages where things have not progressed beyond coffee or wine and the usual yak-yak. I have yet to get in the sack with a guy on the first date and so if it does go further, as any normal woman will, it is a time to size up the man, just like he is sizing me up.
These days politics tends to come up in many conversations and it does not take long to figure which way a guys politics are wired. I have also dated women from time to time and will not date TERFs (trans exclusionary radicals who call themselves feminists). First because I don’t like their politics and second because they would not like the fact I transitioned. I would apply the same restraint with a guy who does not like trans girls.
In my view, however, it is up to the person who does not like trans people to make his/her position known up front so that we can avoid you. Some women are infertile. Some have gone through “the change” or have had an illness such as cancer, and I also suggest you be up front with all women that you are dating in order to impregnate them and generate off-spring. Not every woman, even fertile ones, want kids.
Bottom line is I think it is fine you do not want to date a trans girl and that door swings both ways. Likely we would not want to date you or share our medical histories with you.