The Tennessee State Constitution has a section in it that specifically lists who’s not allowed to hold elected office. You may be familiar with that because here’s Article IX, Section 2:
No person who denies the being of God, or a future state of rewards and punishments, shall hold any office in the civil department of this state.
It’s the infamous section that says atheists can’t hold public office. (Six other state constitutions have similar language.)
Thankfully, that whole section is enforceable, due to the 1961 Supreme Court case Torcaso v. Watkins, but still: That’s what the State Constitution says. Even after that SCOTUS decision, it remained on the books, a vestigial reminder of a more intolerant past.
The reason that section still exists on paper is because there’s a process for amending the state constitution that requires more than a Supreme Court ruling. Lawmakers would need to pass a resolution over two consecutive sessions to get rid of that section, and then voters would need to support that move in a future election.