President Trump recently announced a new rule, issued by the Department of Health and Human Services, that allows doctors, hospitals, insurers and other providers of health care to refuse to deliver or fund services like abortion, assisted suicide or procedures for transgender patients that they say violate their religious views.

The action has been criticized by Democrats and civil liberties groups, with some arguing that it serves as a pretext for discrimination against marginalized groups and threatens to substitute religious views for sound medical advice. But it also invites a larger question: What should doctors do when a patient’s request runs counter to their moral convictions? In medicine we often talk about a patient’s right to refuse treatment. But what about a doctor’s right to deny it?

Such questions have not been definitively resolved by courts or legislatures. The American Medical Association, for its part, is somewhat ambivalent on the issue. The organization’s code of ethics states that physicians have a responsibility “to place patients’ welfare above their own self-interest.” But it also recognizes that doctors are individuals with the right to free choice, stating that “physicians should have considerable latitude to practice in accord with well-considered, deeply held beliefs that are central to their self-identities.” At the same time, that freedom, the code says, “is not unlimited.”