Federal Communications Commission Chairman Ajit Pai tends to dress down when he travels and often wears a hat to obscure his appearance. That’s because of the vitriol directed at him for reducing Washington’s control over the Internet.

On a visit to the Journal today, Mr. Pai wore a suit and tie and maintained his usual cheerful demeanor. But he also reported that the threats against him and his family did not end with the Commission’s December vote to restore the freedom that existed for the Internet’s entire history until...