The COTUS is a civil document that has an amendment protecting freedom of religion and its free exercise thereof. Nothing, not a peep about marriage let alone gay marriage. SCOTUS opened Pandora’s box.
Your answer is pretty weak.
Its part of the job. Either do the job or not. Giving homos marriage licenses is part of the job. I wish it wasn’t. In fact, I wish the states would get out of the marriage business altogether.
But, the world does not grant wishes that often.
She should do her job, or quit. Its pretty simple. Thats how it works in the private sector.