Chrys Stevenson really nails it here.
Now, there's a lot more to say about this issue of conscientious objection in health care, and it won't surprise you to be told that I say a fair bit of it in Freedom of Religion and the Secular State.
But meanwhile, the idea that there is substantial support on a worldly basis for doctors being able to opt out of emergency abortions looks like a myth. Once you remove otherworldly considerations and esoteric moral theories that are deeply entangled with religion, you don't have much basis to object to abortions, much less to emergency abortions. It's not surprising that so many of these doctors turn out to be deeply religious, though it's surprising that so many don't own up to it freely and candidly.