The Freemasons certainly DO exist -- it's not a secret. They have club buildings and everything. It's like a church that never passes out fliers or preaches to anyone or rallies or talks about their teachings. That's all it is. No more an international conspiracy group than Oprah Winfrey's book club. If there are Freemason symbols in DC, then it's because freemason city planners thought it would be cool. That's really about it.
Illuminati, idunno, their existence is plausible but not demonstrable the way the Masons are. And in terms of what they could actually DO, or what their real-world role is, fuck man, idunno, global domination seems like quite the overstatement, but it's not like we don't have an oil lobby. Surely there are plenty of private parties out there acting in their own best interest in the political theater -- is that, in any way, unlikely? No. The only question is how far back could such a group go, and how much success could they really have -- not very far and not much success.