Those words have become common accusations, often tossed about with little or no justification, but have you noticed the disconnect between them? An “-ist” ending “denotes a person who practices or is concerned with something, or holds certain principles, doctrines, etc.,” while “phobic” denotes fear.
The simplest explanation (ISTM) is that it’s hard to come up with a decent -ist word regarding the trans issue. Sexist is already taken, and I don’t believe there’s a word that means something like “believing there are two sexes and you’re stuck with the one you were dealt.”
Still, accusing a person of holding to an (allegedly mistaken) ideology is a different thing from saying a person has a phobia.
Or … is it?
I said “allegedly mistaken” as if this whole thing involves some sort of appeal to truth. But it’s not about truth, is it? It’s really more about (alleged) hatred, and hatred and fear often go together. From that perspective, the words are about the same, in a post-modern sort of way.