How Un-American can you be and still run for President?

In an AP article interviewing Trump supporters one supporter "said she doesn't have a problem applying a religious test to visitors, immigrants and refugees."

Article VI of the United States Constitution states, in part: "...no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States."

The First Amendment to the Constitution reads, in part: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof..."