What about the divorce example? Marriage applications in many states (including NY) ask for plenty of information about previous marriage/divorces. Should a town clerk who is Catholic (or another religion that does not believe in divorce/remarriage) be able to refuse to sign off on marriage licenses where one or both parties were previously married?
License applications ask questions about marriage and divorce for purely legal reasons. The morality of divorce and remarriage (or even marriage—since civil-marriage is not recognized by some religions) is complicated, and its ethics therefore always been seen as the responsibility of the applicants.
Your example is imaginary though, as I’m unaware of any clerks refusing for religious reasons to sign off on legal papers about divorce and remarriage. I know of no Church authorities or religions that would require them to either.
However, signing off on something VERY OBVIOUS, that religious conviction says is always and everywhere highly immoral—an “abomination” using the biblical word, has an order of magnitude difference.... The State is crushing religious freedom when it requires people to approve of homosexual unions.