In the 1950s, when communism was a powerful force in the United States and the world, there was extensive discussion among intellectuals about the appropriateness of letting communist party candidates run for public office. The leading thinker was Sidney Hook.
Since the Left was wishy-washy and lacked even modest logical skills, there wasn't a very interesting discussion because the Left couldn't see any problem with communism.
On the other hand one or two gifted intellectuals pointed out the unfortunate reality that even in a democracy a party determined to destroy the democracy could succeed by getting elected. Today we know of many examples where an elected party has eliminated an incipient democracy. This is true in the Palestinian territories, Egypt, Iran, Russia and Turkey.
Therefore it is reasonable to now ask ourselves whether we should allow Muslims who advocate the destruction of democracy, American legal systems and freedom of religion to run for public office.
I am personally in favor of requiring that all people who run for office must sign a statement supporting democracy and the Constitution lest they be subject to legal removal from office if their actions contradict their signed statement of support.
I realize this is harsh and probably not necessary. Nevertheless it is a subject we need to discuss because we are in a period of hysterical denial about the dangers about modern Islam. (The hysterical denial seems to be most extreme on college campuses.)