@MissFenella
A god complex is an unshakable belief characterized by consistently inflated feelings of personal ability, privilege, or infallibility. ... Someone with a god complex may exhibit no regard for the conventions and demands of society, and may request special consideration or privileges.
I don't think he's got a god complex (though there are plenty of medics who have). He certainly has an arrogant and misplaced confidence in his own judgement but, at the same time, he craves external validation. Like a lot of inadequate people, he is hitching himself to a cause, as a way of achieving that validation. As PPs have noted, it's currently trans rights, but in the past he has sought attention via other causes.
If he had a classic god complex, he wouldn't give a toss about women disagreeing with him - he would feel utterly assured of his own rightness. He is threatened by disagreement because he is weak.
It's also interesting that, as a gay man in the still very homophobic world of medicine, he isn't advocating for other gay men but for a group of which he isn't a member. I would say that suggests low self-worth, albeit teamed with arrogance - the two quite often go together IME: presumably the arrogance acts as a shield for the quivering jelly inside.