In Facebook posts and public appearances, Indian politician T. Raja Singh has said Rohingya Muslim immigrants should be shot, called Muslims traitors and threatened to raze mosques.

Facebook Inc. employees charged with policing the platform were watching. By March of this year, they concluded Mr. Singh not only had violated the company’s hate-speech rules but qualified as dangerous, a designation that takes into account a person’s off-platform activities, according to current and former Facebook employees familiar with the…