At the University of South Carolina, the board of trustees is charged with oversight of the president, reports via Critical Mass. That includes an unusual and surely unconstitutional requirement:
SECTION 59-117-100. President shall not be atheist or infidel.
The board of trustees shall take care that the president of the University shall not be an atheist or infidel.
Harris Pastides, the president of USC, reportedly is Greek Orthodox. At one time, that would have made him an infidel in South Carolina but times have chaged.