Davis and her fellow holdouts are holding their religious duty to be more important than their official duties. That's their right, of course, insofar as they can believe what they like. However, holding a job is not a right. Holding a job requires them to do that job.
I don't know why these clerks chose not to resign their posts, as other, more principled officials have done in other states. However, if they're imagining they'll be remembered someday as heroes along the lines of, say, Oskar Schindler, let me disabuse them of that idea.
Ms. Davis and fellow holdouts, when you lose your jobs, you might be remembered kindly by those who share your beliefs. As for the rest of us, we and those who come after us will look back on you with pity. You aren't saving persecuted minorities from genocide, you're discriminating against people you detest (whether you know you detest them or not). We'll remember you, vaguely, as we do the holdouts against racial equality. We'll remember you as being so deeply invested in an old and unjust way of thinking that you couldn't see how profoundly harmful and wrong it was.
Since you can't bring yourselves to follow the law, you have forfeited the right to hold your job. The rest of us would respect you more if you'd simply quit.