Let me explain something, as quickly and easily as possible.
If you have deep religious beliefs, or deep beliefs of any kind, that conflict with the requirements of a specific position and/or career choice; You have no goddamn right to be in that position.
Are you a vegetarian? Don't get a job in a slaughterhouse and then say that your morals are being compromised by your position. Do you go into epilectic seizures every time you see a Nintendo game? Don't apply for a job at Nintendo as a game tester. You don't believe in a woman's right to choose? Don't become a pharmacist, a doctor, a nurse, or any other health worker who works with women and the choices they make. (You know, like buying birth control?)
I have the utmost respect for anyone's right to his or her own beliefs. It stops at beliefs. Using your position (especially that of a trusted medical professional) to force your beliefs upon others is not acceptable under any circumstances.
What's next? A Christian Scientist ER doc who refuses to treat anyone walking through the door?