The equality act 2010 defines it as:
You can be at any stage in the transition process, from proposing to reassign your sex, undergoing a process of reassignment, or having completed it. It does not matter whether or not you have applied for or obtained a Gender Recognition Certificate, which is the document that confirms the change of a person's legal sex.
I guess if you were in that definition you are transgender, and if you are not, you are not transgender, as far as the equality act goes. If you can be discriminated against on those terms, it’s probably fair to have a selective group on those terms too. But it would have to have a proportionate reason why a particular service would exclude everyone else.
Whether you agree with that definition of transgender, or think it should even be a PC separate to religious beliefs, that’s a different matter.