This is all good and fine, but what do we do when we have heart surgeons saying that heart transplants are against their religion whenever patients are brought to them? What about doctors who start refusing to treat women, because their religion forbids them from contact with women? What about docs who refuse to do emergency abortions, even when it would save the woman's life and the woman consents? Hell, before today, I would have used "What about doctors who refuse to issue the morning after pill to rape victims?"
Yes, doctors DO have freedom, and yes, they do have rights to practice as they want in a capitalistic society. However, this does not give them the license to threaten public health with their own beliefs. Doctors who do not want to issue certain kinds of care should NOT put themselves in the position where the need may come up to issue that kind of care. If he does, he is willfully putting himself in the position where he is endangering the health of his patients. In the end, the liability lies with the doctor, no one else. If a doctor feels he cannot provide the morning after pill, he should not work in an emergency room where such may be requested, or else he can rightly be viewed as a threat to public health.