Steve.. I take a practical view. On easpect of that is that there is no perfect answer.
   There ARE doctors... even OB/Gyns ..who are Catholic, and patients seek out such to share conform with their belief systems. Those who are not Catholic should be careful about which doctors they consult. There should, thus, be a system to advise potential patients about possible conflicts. Now... areas where there will be only a limited selection of doctors (very rural places) should require any doctor to pledge that they will honor the patient's preferences! Thus, Catholic doctors who refuse such limitations should limit their practice to certain venues.
Now, being a practical man, I also realize that this system is far from being reality, so my overriding concern is that no laws be enacted that restrict the rights of patients to have a choice! Several states in the US have used flimsy laws to do as this thread title says and sneak in rules to make abortions almost impossible to obtain, while not specifically ruling them illegal. This must be stopped!
Do you propose a system of laws and a design of a medical licensing setup which will achieve your ideal situation?

(and as an aside, your metaphor about GPs refusing to treat the obese is just not relevant.. ("slippery slope" fallacy)