Kim Davis's defenders are pointing out that she converted to her present faith only 4 years ago, so I'm guessing that she considers herself absolved of prior sins by virtue of that conversion. I have no idea what she considered herself before then.
There is another wrinkle to this case. Davis runs an office with appointed "deputies", who can issue the licenses in her stead. Apparently, since they work for her, she could fire them for insubordination if they issued the licenses without her approval. That's because they were not elected and can be removed without impeachment proceedings in the state legislature. (The next session of the legislature will be in January, and the governor refuses to call a special session just for these cases.) Some of her deputies have said that they are willing to issue those permits, and the judge has said that Davis can go free, if she lets that happen. However, she has forbidden her employees to obey the law. So this is not just personal qualms about herself signing off on the certificates. She is blocking her county government from signing off on them.
Basically, this case is becoming a political football, with Republicans largely getting behind Davis' unlawful behavior or staying silent on the matter. Even Democrats don't want to touch it, because there is a governor's race in progress. The Republican candidate for governor is applauding the illegal behavior and blaming the Democratic opponent for not cracking down on abortion rights, etc. In a conservative state, nobody wants to support the Constitutional separation of church and state.