I beg to disagree with you. This is the issue. Ask Edward Johnson, Puritan contemporary of Mass. Gov. John Winthrop. (if he were alive today :)
"Those who are chosen to a place in government, must be men truly fearing God, wise and learned in the truths of Christ...Neither will any Christian of a sound judgement vote for any, but those who earnest contend for the faith."
So unless you are a Christian you should hold political office. Given the Puritan definition of Christian, most office holders would have to resign.
"The Senators and Representatives..., 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."" The United States Constitution