Let me help answer that question by abstracting away the charged element and disambiguating the most common point of actual logical contention:
Should doctors be forced to perform <P:procedure> they don't ~~condone~~[A:believe is medically safe and appropriate for a diagnosis|B:wish to support or endorse on non-medical grounds].
To me, and for most reasonable people I've properly been able to have a conversation with on this subject, the answer is universally an emphatic NO for the vast majority of possible procedures P, in both cases A and B. However, where things diverge is that most people believe there should be consequences for the doctor refusing on grounds B to perform a procedure other doctors would consider to fit the criteria of A, for virtually every P I've thought of. These consequences typically include removal of their license to practice medicine, and may include civil or criminal penalties in egregious cases where a doctor might claim religious objection to something like CPR in a situation where they were the only doctor working at an ER and the CPR was clearly medically necessary, for example.
Should doctors be forced to perform <P:procedure> they don't ~~condone~~[A:believe is medically safe and appropriate for a diagnosis|B:wish to support or endorse on non-medical grounds].
To me, and for most reasonable people I've properly been able to have a conversation with on this subject, the answer is universally an emphatic NO for the vast majority of possible procedures P, in both cases A and B. However, where things diverge is that most people believe there should be consequences for the doctor refusing on grounds B to perform a procedure other doctors would consider to fit the criteria of A, for virtually every P I've thought of. These consequences typically include removal of their license to practice medicine, and may include civil or criminal penalties in egregious cases where a doctor might claim religious objection to something like CPR in a situation where they were the only doctor working at an ER and the CPR was clearly medically necessary, for example.