I find it wholly acceptable for a physician not to perform an abortion, elective or otherwise. However, I have major concerns when a provider refuses even to refer a patient to someone who will perform the procedure they are looking for. I can imagine as a patient, going to a provider who counsels me about abortion. "Ms. so-and-so (I'm really a Mr.), it is my personal conviction that you should not elect to abort. There are several other options, such as..." That's perfectly fine, but if your beliefs do not sway me and you refuse to give a referral, you've created an extreme hardship for me. Due to the insurance market in our healthcare system, many people don't even have a choice in where they receive care. So no, changing PCPs and providers is not always an option. If a patient is so determined to have an abortion, your moral objection is effectively creating a barrier, which may lead to a back alley abortion, which endangers the mother's life.
There is a medication called PrEP (Pre-exposure Prophylaxis) mostly prescribed to men who have sex with men in order to prevent the spread of HIV. Imagine you are morally opposed to promiscuity and decide not to prescribe PrEP so as not to encourage this behavior. (I realize these are not anyone's stated beliefs in this thread). Is it acceptable NOT to refer the patient to someone who will prescribe this medication?