She Can't Do That
A county clerk does not have the right to ignore laws that violate her conscience. She has the right to quit her clerk job, but she doesn't get to decide policy. If there's one thing that bugs me more than an overzealous court assessing the political winds and choosing a popular side, it would be an obstinate government bureaucrat believing she gets to dictate local policy based on her religious convictions. Get her out of there.