Alex, a 23-year-old Sunday school teacher and babysitter, was trembling with excitement the day she told her Twitter followers that she had converted to Islam.

For months, she had been growing closer to a new group of friends online — the most attentive she had ever had — who were teaching her what it meant to be a Muslim. Increasingly, they were telling her about the Islamic State and how the group was building a homeland in Syria and Iraq where the holy could live according to God’s law.

One in particular, Faisal, had become her nearly constant companion, spending hours each day with her on Twitter, Skype and email, painstakingly guiding her through the fundamentals of the faith.

But when she excitedly told him that she had found a mosque just five miles from the home she shared with her grandparents in rural Washington State, he suddenly became cold.

The only Muslims she knew were those she had met online, and he encouraged her to keep it that way, arguing that Muslims are persecuted in the United States. She could be labeled a terrorist, he warned, and for…