Seems to me they'd have to. You can't have it both ways -- if you have a religious right that may directly influence a course of treatment you may or may not propose and/or carry out, I as the patient should have the right to be fully informed as to where your influences are coming from.
Alternatively, if some doctors want freedom of religion, and that religion precludes them performing some of the duties of being a doctor, maybe the correct resolution of this conflict is for those people to recognize they can't be doctors in Ontario.
It is one thing to say "I don't believe it is right for me to do this" and quite another to say "I don't believe it is right for anyone to do this". Your right to swing your fist ends at my nose; in this case the practice of these religions is affecting other, probably non-practitioners, and I think that the right to practice your religion ends at my health care.