Donald Trump evoked outrage from across the political spectrum Monday by calling for a “total and complete shutdown” of Muslims entering the U.S., a proposal that taps into voter anxiety about the recent spate of terrorist attacks yet likely runs afoul of religious freedoms enshrined in the Constitution.

“It is obvious to anybody the hatred [among Muslims] is beyond comprehension,” Mr. Trump said. “Where this hatred comes from and why, we will have to determine. Until we are able to determine and understand this problem and...