Orac hits the nail on the head here. I don't really care about what religious beliefs my healthcare practitioners have. No one except their co-religionists really does. But, when those religious beliefs start to impinge on their profession -- then I care.
When one becomes part of a profession, whether formally (e.g., medicine, pharmacy, law, accounting) or informally (e.g., philosophy, biology, education, police) organized, then one accepts certain obligations and abandons certain rights, in exchange for certain powers or "arcane" knowledge. For example, physicians have the power to prescribe medications -- this is a power. In return, the physician is obligated to provide those medications in order to best serve the physical health of their patients. Similarly, a pharmacist is given the power to dispense medication, and, in return, must take on the obligation to dispense the medication in accordance with the orders of those professionals who are licensed to prescribe it.
I find it utterly bizarre that there are people who believe they can have these sorts of generally-restricted powers without any corresponding obligations being taken on or rights being given up. The powers come with costs -- that's made, I would have thought, pretty clear before becoming a member of the profession.
What I find really horrific is one of the cases Orac cites, wherein a state medical board upheld the decision of a GP to refuse to provide a general physical examination for a single woman who was trying to adopt a Mexican child (the GP's excuse -- it was emphatically not a reason -- was that children "should" have two parents; that's a blog post in itself).