Depending on what time sundown occurs, most clerks offices already are closed during those hours.
There are laws about accommodating reasonable religious requests, so if an office where open the clerk could certainly ask not to work those hours. Just as in this case, she is asking to not sign the licenses, a reasonable accommodation.
Nice strawman though.
Not a straw man at all.
County Clerks here are open Saturdays to accommodate people who cannot get there M-F.
What about a Jew who wanted the office closed on the High Holy Days, a Muslim who wanted it closed every Friday, me who would it closed on the first day of every Hunting and Fishing Season?
Someone also asked about a devout Catholic refusing to issue marriage licenses to those previously married whose previous marriage was not annulled?
The word “peasonable” in a contract is a word that makes many lawyers rich. Religion and law mix very poorly.