I'll start with an admission that might surprise you. For this evangelical Christian opponent of gay marriage, the Kim Davis question is not clear cut. On the one hand, I absolutely do not think the law should compel her to issue licenses for gay marriage. I also have a very big problem with the way this law was established, which was by no legislative process at all.
But: She is an elected official of a secular institution, and she takes an oath to enforce the law - although the law imposed by the Supreme Court was not the law when she decided to run for the office. Even so, laws change all the time and no elected official can say, "Hey, if I'd known that was going to be the law, I wouldn't have run!"