If Muslim men are going to let their personal observation of sharia get them upset with gummit clinics that have laxer policies, by cracky let them boycott those clinics. But this sounds like a slam dunk first amendment case. (The doctor may still wish to enter private practice, where this kind of bull hockey does not prevail.)
That would be nice if it happened in America, but this is Detroit we're talking about.
(sarcasm)(or is it?)