It occasionally happens that I agree with Lindsey Graham, and this is one of those times. He says that if Kim Davis feels she cannot carry out the responsibilities of County Clerk of Rowan County, Kentucky, she should resign. (Personally, I don't mind if she uses up her vacation days while she's in jail — it's the kind of thing vacation days are for.)
Her mother was county clerk for thirty-seven years, and Kim Davis worked under her mother. Her son works in the office now, and probably expects to be elected to his mother's job when she's ready to retire. That's small town politics. It's extremely likely she ran unopposed, or against some token Republican candidate. (Yes, Kim Davis is a Democrat.)
Some states are enacting legislation which would allow public officials to refuse to perform their duties when those duties conflict with their religious convictions. We can be quite certain that such laws will be invalidated by Federal courts, but the process is likely to drag on and on, and get pretty boring before it's over.
Catholic judges can't refuse to issue divorce decrees, and Muslim postal workers can't refuse to deliver copies of Playboy because the centerfold isn't wearing a hijab. As Donald Trump says, this is a nation of laws. I hope Ms. Davis enjoys her moment of celebrity, but the chief significance of this particular instance of conscientious objection is that it is further splitting the Republican party.