Any American can run for political office if he/she has enough money, a basic knowledge of politics, a fair education and a talent for speaking in public. You can be gay/lesbian, black, oriental or even physically disabled. However, you must have religion and a Christian one at that. I don't think a Muslim is acceptable unless he/she is a bonafide peaceful Muslim and has spoken out against terrorists.
You can be all these things, except being an atheist. Public distrust of non-believers is not the only reason atheists very seldom run for office. Running for a seat in state legislatures as an atheist is actually prohibited in some states. It is illegal according to the state constitutions of Tennessee, Arkansas, North Carolina, South Carolina, Texas, Maryland, and Mississippi.
It will change eventually. It will change soon.