Courts are pretty good at awarding large dollar amounts and/or throwing people in jail when they lie to the court. Which is what would be required if someone attempted this, since (as far as I'm aware) there's no religion or cult in history that believes anything remotely approaching this very strange straw man.

Nope. That will not work because the bill says services not people.

The doctor can prefuse to perform specific services, nothing in the bill permits then to refuse to treat specific people.