Since everyone seems obsessed with healthcare issues related to sex, let's try another one and let the pro and con sides argue their points:
The setting is an ER in a small town. A trauma comes in. The patient is in hypovolemic shock and has already gotten a 2 liter bolus of saline in the field but still has a weak pulse and unstable vitals/decreasing blood pressure.
The ER has 4 bags of type O blood ready to transfuse when the patient arrives.
However, the physician covering the ER that night recently converted to be a Jehovah's Witness and refuses to transfuse the patient because he believes it violates his religious beliefs. The patient expires before another physician can be tracked down.
Did he have a right to refuse the transfusion.
He did not.
However, trying to compare this to religious objections over religious groups being forced to provide birth control and abortions is like comparing apples and oranges.
Forcing a doctor, as the federal govt, to violate their religious beliefs is a violation of the seperation of church and state.
Solution? The hospital doesn't hire certain doctors due to the fact that their personal ideology prevents them from performing all the duties of the job...in your example no jehova's witness who are not willing to forgo the transfusion belief can be hired.