I think it’s conceding too much to base a right to refuse on religious faith.
Like, what about a surgeon who refuses because he recognizes and accepts reality?
If that surgeon is not protected, no one is safe.
Reality is a theological construct. Even if the doctor is an atheist, who adamantly denies the existence of a deity, he still believes that reality is objectively provable, and thus a person with a penis is a man, and a person with a vagina and mammary glands is a woman. And woke-ist deconstructionists believe that reality is a matter of opinion, and everyone has their own, personal truth. So if you were born with a vagina and feel like identifying as a man, well, damn! You have to have those mammaries and other indoor plumbing stuff removed, and a bit of bicep somehow made into a facsimile of a penis, even without the prostate gland, testes, and other stuff that men are both blessed and cursed with. You feel manly, so you’re a man. And the same the other way.