From all that I have read these are/were real. They weren’t intended to be aggressive or cult clans bent on violence or anything of that sort. They were just well known groups. I’m personally intrigued by the Illuminati. Thanks to the great Dan Brown and his novels who have made me want to go to the Vatican and other parts of Italy.
Perhaps they started out as frat groups but back in the day when these groups weren’t in every college or school, they got people from high ranks to be a part of them. That kinda elevated them from being just a frat group to something more important. They actually are believed to have immense weight to their titles and names.