Kansas City, Mo.

President Trump made Turkey’s imprisonment of the American pastor Andrew Brunson a cause célèbre, but why was he arrested to begin with? According to a Turkish indictment, he supported terrorist groups and posed a threat to national security. Rumor had it Mr. Brunson—an Evangelical Presbyterian Church missionary—maintained nefarious ties to the Mormons, the Jehovah’s Witnesses, Kurdish separatists and the Islamic Gülen movement

Mr....