Certainly it's debatable if doctors should be able to deny treatments they think aren't harmful but they see as religiously offensive. But the root disagreement

Certainly it's debatable if doctors should be able to deny treatments they think aren't harmful but they see as religiously offensive. But the root disagreement here is primarily about harm, and we already have agreed as a society that doctors have a duty to not knowingly harm their patients. If you can frame something as a civil rights issue, that can help resolve some conflicts but doesn't do much in terms of resolving contentions around if a specific procedure is harmful to a patient or not. In medicine, it does simply boil down to either persuading physicans that the procedure isn't harmful, or determining as a society we will no longer accredit people as physicians if they believe it is harmful.