When 14-year-old Brian O’Neill of Washington, D.C., wanted to find out what his friends had been up to over summer vacation, he did something radical: He asked them. Unlike most kids his age, Brian isn’t on social media. He doesn’t scroll through his friends’ Instagram shots or post his own, nor does he use Facebook or Snapchat. “I don’t need social media to stay in touch,” he says.

Such abstention from social media places him in a small minority in his peer group. According to a 2015 report by the Pew Research Center, 92%...