"Non-moral reasons" is shorthand for reasons that do not involve morality that is not intrinsic to performing the duties he is being paid for. For instance, "I refuse to give the patient drug X, because drug Y will cure the patient and drug X will not" is a moral reason insofar as wanting the patient to be cured is a question of morality, but it would be okay. "I refuse to give the patient drug X because God tells me not to give people drug X" would be an unacceptable reason. This actually happens for contraceptives.

One solution is to prohibit such doctors from practicing medicine. Another solution is to permit them to opt out for moral reasons, but only if

1. There is some reasonable way for the patient to know in advance, and
2. Circumstances are such that the doctor's opting out doesn't make it too much harder for the patient to see another doctor who will provide such prescriptions

Letting people buy all medicine freely has its own problems because the doctor's refusal to prescribe also implies the doctor refuses to use his expertise to tell the patient what medicine he needs.