Performing abortions requires special skills.

Performing euthanasia (or, as in your other example, cooking kosher meals) doesn't? Baking cakes for gay weddings does?

(FWIW, I don't think that bakers should be forbidden by law from refusing to bake cakes for gay weddings.)

Thus it would make no sense to force doctors who aren't trained for the procedure to perform it.

The fact is, I heard that in said major European country you sometimes get the same doctor refusing to perform abortions in public hospitals ostensibly for moral/religious reasons but who has no trouble whatsoever with them in their own private practice.