The Hippocratic Oath does not allow doctors to perform abortions. 
it also doesnt appear to allow them to practice any of the modern religeons ..
I swear by Apollo, the healer, Asclepius, Hygieia, and Panacea, and I take to witness all the gods, all the goddesses, to keep according to my ability and my judgment, the following Oath and agreement:
SoR_AWC
You took an oath so you could heal people. The reforms we're proposing will help you live up to that oath."
like they aren't living up to it now.