The notion that a health service provider should be forced to honour a patient's request to die represents one more step on the path to one-size-fits-all thinking that has produced so many state sponsored sins in the past that it is difficult to imagine any civilized state still imagines this to be appropriate.

States make bad decisions often enough that it warrants leaving choice on the table for as many parties to a transaction as there are.  It is important to leave space for the dentist who refuses to mine gold out of a cadaver's mouth, or the surgeon who objects to performing deadly experiments on humans, because without that space, they can plead that they were just following orders. 

The patient can choose to go elsewhere if a service provider objects to ending their life.  It may not be easy for the patient, but no self-respecting professional sworn to noble objects should be forced to comply with arbitrary state-sanctioned dictums on legitimate matters of conscience.