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 abortions they don't condone?
No person should be forced to perform actions they don't condone.
But there is no unalienable right to be a doctor. If someone wants to be a doctor and not perform health care procedures, then that's not compatible with being that kind of doctor.
They are entirely free to switch careers to do something else.
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.