If a physician was required to perform abortions there would be outrage -- this is no different at all.
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Of course it is different.
The comparison just doesn't work. It is obvious to all that doctors specialize in certain types of procedures. A doctor who performs abortions wouldn't need to be forced to do so. A doctor who for whatever reason chooses not to do that kind of procedure would never be "forced" to do a procedure for which they are untrained.
Isn't there a law in New York that all medical school students be trained to perform abortions?