What are they going to do, force a doctor's hand to abort? When, in the concept of liberty, did it become proper to force another autononomous individual to act against their conscience, in the absence of clear and present danger?
The easy answer for the docs is not to be qualified to perform them. GPs don't do abortions, nor do allergists or dermatologists.
IIRC California, seeing the dropping number of doctors qualified to do abortions tried to mandate the training. Not sure where it went.