IANAD and don't have a great source for this, but I've both heard and read about some variety of "professional code" or "best practices" where MDs are expected to leave their personal convictions aside when deciding and prioritizing who gets what care.

I may personally agree with the exact situation you describe, but relying on "common sense" breaks fast at scale. If the doctor(s) making the call are devout adherents of some religious sect, would you prefer that they prioritize the drunken driver above the pregnant woman who needs an abortion of the child that was conceived out of bedlock?

Or denying care to the heroin addict ODing?

IMO, completely removing moral judgment from the medical evaluation process is a net positive.

This doesn't have to mean "first come, first serve", and I assume it doesn't in most places.

I agree, so long as we’re not expecting doctors to do triage, which I believe they generally don’t. Triage is generally don’t by specially trained nurses, as I understand it.

I meant “generally done by”

Can we trust a nurse who refuses to be vaccinated to do the Right Thing at this moment?