I think that most of the paranoia of these groups, theories and actual conspiracies, come from a different age - when access to information was truly an exclusive commodity.
I can see truth to the currents theories if applied 60, 80, 100 years ago. (In the USA)... There was still the need to believe and to ensure that American WASP "culture" was superior. These groups and clubs, like the Klan, mostly have their roots in a turbulent time in America's history as a way to exclude people as much as to include only WASPs.
Now, quite honestly, there are enormously rich, powerful and influential people of diverse backgrounds just in the USA - not even mentioning Europe or Asia. There may have been a time when many of the strings to power were held by members of these groups, but, based on their founding core beliefs, if they really followed them, they would not have Colin Powell, Condoleeza, Wolfowitz and co elevated to such high helping positions. (Interestingly, Wolfowitz is connected to radical right wing Israeli groups, but that's another discussion.)
My point is, though there may have been a time when you had to pass WASP approval to succeed (more easily) in business and politics a long time ago, now, there are equally (if not more so) valuable and important paths that completely bypass their old boy networks.
Anti-semitism, anti-black, anti-poor, anti-west of Philly keeps these leftover relics in their own little world more than the walls of their clubs. It's just bitterly ironic that they continue to surround themselves with the same wood panelling, the same oil paintings, the same drab food, the aversion to wine, the love of grain alcohol, the same wool and cotton fabrics and patterns - in a hope to imitate the English culture that they historically despised to much.