In discussing the schism caused by the Boy Scouts deciding to allow gays in their leadership, Walt Longyear is quoted as saying, “Under the Constitution, your conscience trumps everything.”
This is not true under any understanding of the Constitution of which I am aware. As everyone’s favorite conservative Supreme Court justice wrote in the majority opinion in Employment Division v. Smith (1994): “To permit this would be to make the professed doctrines of religious belief superior to the law of the land, and in effect to permit every citizen to become a law unto himself.”
You can be bound by the direction of your conscience. But if your actions contradict the law of the land, you are subject to legal sanction. Conscientious objectors can refuse to take up arms in time of war because of their beliefs, but cannot sit on the sidelines.
There is no “Get Out Of Jail Free” card, despite how they do things in Kentucky.