Separation of church and state is the law of the country. Her personal beliefs shall not trump the law as she is a public servant and she swore she would uphold the law of the country.
Kim Davis actions reminds me of the "conscientious objector" phenomenon. I admire her conviction but do not believe she has the right to apply her own moral judgement to an official government process. She has the full right to debate gay marriage as an individual, but not as a county clerk.