When fellow believers in Sweden first began coming to him with information from the Internet that contradicted the church’s history and teachings, he dismissed it as “anti-Mormon propaganda,” the whisperings of Lucifer. He asked his superiors for help in responding to the members’ doubts, and when they seemed to only sidestep the questions, Mr. Mattsson began his own investigation.

But when he discovered credible evidence that the church’s founder, Joseph Smith, was a polygamist and that the Book of Mormon and other scriptures were rife with historical anomalies, Mr. Mattsson said he felt that the foundation on which he had built his life began to crumble.

Around the world and in the United States, where the faith was founded, the Mormon Church is grappling with a wave of doubt and disillusionment among members who encountered information on the Internet that sabotaged what they were taught about their faith, according to interviews with dozens of Mormons and those who study the church.

“I felt like I had an earthquake under my feet,” said Mr. Mattsson, now an emeritus area authority. “Everything I’d been taught, everything I’d been proud to preach about and witness about just crumbled under my feet. It was such a terrible psychological and nearly physical disturbance.”