She can cite Scripture (many, many passages) indicating that sodomite behavior is abominable. Giving sanction to that behavior would be formal cooperation in that abomination.
Can you perhaps cite Scripture (not just God's word, but any major religious texts) that assert that issuing a drivers license to an otherwise competent person would be a formal cooperation with evil?
How about if you wanted to get a permit to put an addition on your house and the city official denied you that?
This already happens. If a person, for example, wanted an addition on their house in order to accommodate religious worship, there are many examples where building permits were denied because they'd create a zoning problem.
Do you usually exercise your right to vote? Maybe you’d like to experience being told you can’t register to vote because some public official says that God told him you were a sinner.
My above question applies here: can you cite some religious doctrine that arbitrarily denies a person the right to vote based solely upon a religious rationale?
On the other hand, all this self righteous woman needs to do is perform the task she was elected to do and fill out some paperwork. No harm done.
You, FRiend, need to study up a little bit on the subject of moral theology, specifically, the concept of formal and material cooperation with evil.
An Amish clerk might think so. A Quaker clerk might think issuing a gun permit is formal cooperation with evil. A Catholic clerk might think that issuing a marriage license to someone who is divorced is formal cooperation with evil.