Unfortunately, that makes Kim Davis a criminal, and she is subject to censure by the State. And I’d never suggest that the State not do its job in that regard. But nor can I see how Kim Davis could do anything other than what she has done. I would do exactly the same thing.
Sadly, I’ve seen many good Christians say things like “why doesn’t she just resign?” I’m afraid I vehemently disagree with that option. You might have some case to say that had Davis been elected after Obergefell, and not been honest about her stance, that holding her position is untenable. And certainly in the private sector, I’d argue that if you are someone who doesn’t want, say, gay sex occurring on your property, then maybe you shouldn’t be running a bed and breakfast! But that argument doesn’t hold when it comes to the government. I’ve always said that gay “marriage” in itself is something that is none of our business. There’s no question that a gay couple should have the right to find a church willing to perform a ceremony for them, invite a hundred of their closest friends and make some vows to each other. But when you start asking the government, an institution that I participate in as part of a democratic society, to positively sanction something and certify it, and furthermore, to misrepresent the truth about it against the beliefs of a significant part of the population; that discriminates against the truth, and against me personally, as someone who holds to that truth. You exclude me, and others like me, from even participating. That violates our rights. Why should anyone have to resign over that?
Of course, as a Christian, I don’t have rights. I don’t say that ironically or sarcastically, I really mean it. I should have no expectation of fair treatment from the world at all. Christ certainly never got it. But when you are elected to do a job, and the State quite literally makes the honest and faithful exercise of that job illegal, the correct response is not to let the State get away with it, but stand your ground. In the Book of Acts, the Sanhedrin told the Apostles not to speak about Christ, but none of them resigned. Instead, they said “Whether it is right in the sight of God to listen to you more than to God, you judge. For we cannot but speak the things which we have seen and heard.” Kim Davis, faced with being told not to speak the truth, can do no less.
I’m sure many will take issue with my view of “the truth” and see it as subjective. I’m afraid I do indeed believe in such a thing as objective truth, and moreover, that there are few things in life more basic than the truth of what marriage is. It’s a union between a man and a woman, sure as penises and vaginas fit each other like a jigsaw puzzle. To quote an obscure first century philosopher…
…from the beginning of the creation, God made them male and female. For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh; so then they are no longer two, but one flesh.
Marriage only exists because we have two different sexes. The State wants us to believe and act otherwise. The State is wrong. We cannot say otherwise, because that way lies madness. And we will take whatever punishment the State deems appropriate for this infraction with gladness.