What she is modestly calling “personal religious beliefs” have a larger stature in classic American political and legal thought. She, in fact, is believing in the same God, with the same standards, that the Founders acknowledged.
If anything she’s too weak about it here. She has the right to say this is wicked in the absolute and there is a long line of reasoning that such “law” is simply invalid.
Saying it’s about the money is kind of laughable. I don’t imagine Kentucky state clerks get a king’s ransom and the likely upshot of this if she keeps it up would be to get dismissed by legislative action.
So anyhow, millions of people now agree she is standing up against what is wicked. And really she is, even if not with quite the words that might please you and me.
The reason government actors must always follow the law is that the law is the source of their authority to act in a government capacity in the first place. Thus a 9th Amendment objection - based in the rights of the State of Kentucky, the government she works for - would be a lawful one, but her 1st Amendment argument - a right of private citizens -is not.
If her grounds are religious grounds then she cannot assert them over her actions as a government actor, just like Lois Lerner cannot lawfully assert the Fifth to hide her actions as a government actor.