Former Godfather's Pizza CEO Herman Cain is not a first-tier presidential candidate. He is, however, actively running, and he does have real support. He won a straw poll at the Conservative Principles Conference in Iowa over the weekend, and last month won another straw poll at a conference organized by a tea party group.
That substantial support makes it all the more remarkable that Cain told Think Progress' Scott Keyes over the weekend that he would not appoint a Muslim to his cabinet.