I was baptized into the same church as hers.
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Then you should know better.
A man and a woman want marriage license. Perhaps one (or both) has been divorced. Perhaps the woman has an out-of-wedlock child. Neither of these are beyond forgiveness with true repentance.
There can be no repentance between two men or two women getting “married” - unless they do not get married at all.
How can there be true repentance if you continue a sinful lifestyle?
Jesus Christ defined marriage as a lifelong union between a man and a woman. In Matthew and in Mark, Jesus is quoted as saying that if a man divorces his wife and marries another then he is committing adultery. Same with a woman divorcing her husband and remarrying. So if we can certainly agree that same sex marriage is not a marriage in the Biblical sense of the term then by the same token neither is Kim Davis's current marriage. Or the one before that. Or the one before that.
My point is she would without question issue a license to one or both who did not bibically divorce and then remarried. They would be living in adultery until that ended. I'm not a scholar, but don't you have to stop sinning in order to repent? Would that mean ending an adulterous marriage? Scripture doesn't address that.