It's not about her 'believing' whatever the hell she wants. It is about not doing her job, being ordered by a judge to do her job, and refusing the judge's order is what got her put in jail. The clerks job is to process the license, not decide who gets to have one.
Let me put it another way. Your county elects a sheriff. Your state has a 'shall issue' concealed carry permitting law. Your sheriff refuses to process your concealed carry permit on account of his pacifist religious teachings. This government functionary is now claiming he has the religious right to deny you your rights. Judge orders him to issue the permit, but refuses and is jailed on contempt. Is he being jailed for his religious beliefs, or is he jailed for defying the judge's order to carry out the law and issue your permit?
We're not a nation of laws, except for when the county clerk of Podunk decides to no longer follow the law. We're a nation of laws, period. The other choice is an anarchy where every bureaucrat you encounter can decide which laws apply today. No thanks, I can't imagine a worse tyranny.