The state of Tennessee used to have a law that banned members of the clergy from running for public office. The U.S. Supreme Court in 1978 rightfully declared this provision unconstitutional.
In the United States, pretty much all adults, with very few exceptions, have the right to run for public office. I wouldn’t have it any other way. If democracy means anything, it means the right to choose our own leaders. Disqualifying people from the ballot because of their race, gender or religious beliefs is un-American.