This was Jim DeMint's signature issue back in 2004 (okay, that's an exaggeration, but he had this exact same position).
WISTV, Oct 6, 2004
In a debate Sunday with Democrat Inez Tenenbaum DeMint said openly gay people should not be allowed to teach in the state's public schools.
DeMint defended that remark during an interview with the Aiken Standard on Tuesday and said he would feel the same way about single, pregnant women who lives with a boyfriend teaching a third grade child. He said teachers should be held to a higher moral standard.
Now, of course, in the above link it says he apologized-for the remark about single, pregnant women. Not, heaven forbid, about openly gay teachers.
Apparently, though, he's walked this one back.