Last Easter, Jamie Paulin-Ramirez, a 31-year-old mom with a $30,000-a-year job as a medical assistant, announced to her family that she had converted to Islam. A few months later, she began posting to Facebook forums whose headings included "STOP caLLing MUSLIMS TERRORISTS!"

On Sept. 11, she suddenly left Leadville, Colo., a small town in...