HPA-AN, Myanmar—The Venerable Wirathu hitched up his orange robes, stepped up onto a stage on a recent Sunday and tapped the microphone.

“What kind of people are these Muslims?” he barked as a crowd of 1,000 in this small town east of Yangon cheered him on. “Do they eat rice through their backsides and excrete through their mouths? They are the opposite of everything in nature.”

Ven....