County clerks in Kentucky are still refusing to issue marriage licenses to same-sex couples, saying it violates the clerk's personal religious freedom, even after a federal judge ordered them to, explaining that the clerks have the right to exercise their religions in their own lives, but not to impose it on anyone else.
If they could, they could also deny a business license to a store that's open on Sunday. Or an Orthodox Jewish police officer (granted, not a large group in Kentucky) could ticket someone for driving a car on Saturday.
If your beliefs make it impossible to properly carry out the responsibilities of your job, that's on you -- get another job. The irony is that politicians in southern states have made a lot of noise in recent years worrying about the imposition of extremist Sharia law. But extremist Christian law? No problem.