In the United States there is an unwritten rule that if you don't hold the belief in "God" above everything else, you don't have a prayer to a hold a major office in the United States. Despite the idea of an "unwritten" rule, some states actually have it on the books.
There's never been an atheist, agnostic or non-religious person to ever be elected to the White House and it's almost non-existent in Congress or in most public offices. Rep. Pete Stark (D-Calif.) left office in 2012 as its only openly atheist in office. Former Rep. Barney Frank (D-Mass.) also came out as an atheist but was retired when he did so. Frank came out as Congress' first openly gay member in 1987, but was too nervous to admit his atheism, which in itself says enough about the stereotype of being a non-believer.
The Washington Post recently pointed out eight states that have a state constitutional ban or limitations on atheists and non-believers holding office. The Post also points to a 1961 Supreme Court case that limited the state's restrictions on atheists holding an elected position, but nonetheless, the laws are still in place. Below is a list of the eight states that have limitations on those who don't believe or subscribe to a religious belief.
Arkansas, Article 19, section 1:
“No person who denies the being of a God shall hold any office in the civil departments of this State, nor be competent to testify as a witness in any Court.”
Maryland, Article 37:
“That no religious test ought ever to be required as a qualification for any office of profit or trust in this State, other than a declaration of belief in the existence of God; nor shall the Legislature prescribe any other oath of office than the oath prescribed by this Constitution.”
Mississippi, Article 14, section 265:
“No person who denies the existence of a Supreme Being shall hold any office in this State.”
North Carolina, Article VI, section 8:
“The following persons shall be disqualified for office: First, any person who shall deny the being of Almighty God.”
Pennsylvania, Article 1, section 4:
“No person who acknowledges the being of a God and a future state of rewards and punishments shall, on account of his religious sentiments, be disqualified to hold any office or place of trust or profit under this Commonwealth.”
South Carolina, Article XVII, section 4:
“No person who denies the existence of a Supreme Being shall hold any office under this Constitution.”
Tennessee, Article IX, section 2:
“No person who denies the being of God, or a future state of rewards and punishment, shall hold any office in the civil department of this state.”
Texas, Article 1, section 4:
“No religious test shall ever be required as a qualification to any office, or public trust, in this State; nor shall any one be excluded from holding office on account of his religious sentiments, provided he acknowledge the existence of a Supreme Being.”
Though the above state's have a ban in their state constitution, the United states constitution specifically notes that no religious test shall be required to hold public office.
Article Six of the United States Constitution:
"The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States."