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There are a number of fraternal organizations with mystical trappings; in America, the Freemasons and the Shriners are probably the best-known. Is there any SR book that talks about their reaction to the Awakening?
Threats, Threats 2, and all magic books after Magic in the Shadows. The Black Lodge is the most important in the fluff, being behind pretty much al the evils of Washington and whatnot, and (arguably) backed by the third major type of Immortals in Shadowrun, next to dragons and elves.
Hermeticism is a good fit if you consider freemasons tied to jewish conspiracies (Quabbalism would also fit reasonably well then). If you want to be more historical, use Christian Theurgy (p. 44 Street Grimoire/p. 37, Street Magic). If you want to go full 80s Satanist Scare on the Freemasons, you can also use Black Magic (p. 41 SG/p.36 SM) or a toxic tradition of your choice.