There was an interesting thread about freedom of religion the other day. You are correct: the Constitution trumps excluding anyone from office or discharging a public function on account of religion. It's pretty damn clear in black & white, carved in marble.
But I don't think the Founders meant much more than that Catholics, Methodists and Baptists were the ones who should not be excluded. And that we ought to tolerate the occasional law abiding Hindoo, Jew or pan-spiritual savage in our midst. Please forgive the sarcasm.
This in all seriousness, however: the Founders did not live in the world of 9/11. It's time to amend the Constitution. "Members of violent and terrorist cults shall be disqualified from Office or public Trust under the United States."
Seriously, Why do so many of you keep calling Islam a religion?