When Walter Wilson, a construction worker from North Carolina, sat down to watch the blockbuster “Avengers: Endgame” on Amazon Prime Video, he ended up seeing something very different: a 2007 documentary, also titled “Endgame,” directed by far-right talk show host Alex Jones.

Mr. Jones’s videos have been banned from many mainstream sites like Apple Inc.’s iTunes and Facebook for promoting outlandish conspiracy theories. “Endgame” purported to document a clandestine organization of bankers and politicians bent on establishing...