Look at it this way: if someone was drafted into the army and that person held a deep religious belief against violence and the taking of another life (a Quaker, for example), that person would be recognized as a conscientious objector and assigned to a non-combat role, typically a medic.
That's what Kim Davis is: a conscientious objector with respect to gay marriage. She should either resign or ask to be assigned to a different job within county government. You wouldn't assign a conscientious objector to a combat role and then allow him to refuse to do it and be protected by a "religious freedom" act. You don't allow a pacifist to refuse to fuel a bomber because it violates his conscience. You don't allow one member of an artillery crew to do everything but anything involving the loading, firing, targeting, transportation, or maintenance of artillery while still remaining on said crew.