Secret societies have an air of mystique around them, but often they're just social clubs with extra steps. People are social creatures, and having something to belong to is healthy for most!
Leonard Leo, who's had more influence over the selection of Supreme Court Justices than just about anyone, belongs to a Catholic secret society. It's not silliness or paranoia to worry about groups like these.
There have been real secret organizations, but they tend to be more like terrorist groups. The League of Free Jurists, the Irgun, etc. Ones that work as lobbies have to have some visibility. You can't stay completely behind the scenes forever and accomplish much.
The U.S. Chamber of Commerce is arguably one such. Its existence is not a secret, but its 1970s plan to make the US more friendly to corporations didn't become known until it had already worked.