If the county clerk in question was a Muslim woman who didn't want her name on same-sex marriage licenses, we'd hear the old "just shut up and do your job" spiel they give the rest of us.
I'm sure some on the regressive left would defend her.
Doubtful. I remember a story on DU about a Muslim flight attendant for a small regional airport that was fighting to be able to refuse to serve alcohol on flights (she had already worked the job for awhile and had done so but now converted to Islam.) Everyone was against her and demanded she just do her job.