I think you're reading it wrong. I think it's supposed to stop people from interfering with other people's constitutional rights, and it's worded ambiguously. Better wording would be: If two or more persons conspire to injure, oppress, threaten, or intimidate any person in any State, Territory, Commonwealth, Possession, or District in order to to prevent the free exercise or enjoyment of any right or privilege secured to him by the Constitution or laws of the United States, or because of his having so exercised the same;