To be fair to the people of Tennessee, atheists are not the only ones banned from running for office, nevermind the obvious unconstitutionality of that measure (something about a so-called 14th Amendment, blah, blah).
Note that the measure applies to deniers of the "future state of rewards and punishment," which basically excludes everyone who's not Christian or Muslim. So Conn. Sen. Joe Lieberman can't run for office in Tennessee.
Clergymen, the Constitution further says, can't hold office in the state's Legislature. That takes care of former Arkansas Gov. Mike Huckabee.
To boot, people who hold duels can't run for office either, which makes one wonder just what the Dickens is going on in Tennessee.
That, as you know, would have banned Founding Father Alexander Hamilton from running for office in the state, if only he weren't killed by Vice President Aaron Burr.
And that's why Tennessee ends up with people like Al Gore.
But don't take my word. Take the word of the Constitution of Tennessee: