Late last August, a 40-year-old cleric named Salem Ahmed bin Ali Jaber stood up to deliver a speech denouncing Al Qaeda in a village mosque in far eastern Yemen. It was a brave gesture by a father of seven who commanded great respect in the community, and it did not go unnoticed. Two days later, three members of Al Qaeda came to the mosque in the tiny village of Khashamir after 9 p.m., saying they merely wanted to talk. Mr. Jaber agreed to meet them, bringing his cousin Waleed Abdullah, a police officer, for protection. As the five men stood...