Perhaps I have a slightly different take on this. I tend to be conservative but not very religious. That being said , I think the conflict is between 2 things:
1) The SCOTUS ruled that gay marriage is permissible and cannot be denied BY LAW. Is gay marriage THE LAW in Tennesee? The SCOTUS CANNOT write law, that takes the US or state legislatures. So, is she in jail for "breaking" a law that probably DOES NOT EXIST.
2) From her religious objection, she holds a position that now or shortly would require her to issue marriage licenses to gays. She does not have to perform or attend ceremonies. She does not have to bake their cake. She does not have to agree with their "sin". I'm sure she has issued many marriage licenses to other "sinners"--adulterers, drunk drivers, shoplifters, etc. All she has to do is her job. And if she needs religious clarification, even Christ told the people to "render unto Caesar that which is Caesar's"---so it looks like Jesus expected his followers to follow man's law as well as God's