What I have found over the years is that there is no “left or right” in the conspiracy. The bigger picture has no actual party affiliations that affect their operations. Joint operations and common end goals supersede party labels or loyalties.
There are so many conspiracies and conflicting motives and so much disloyalty that the small, quick, and venal tend to consume the large and lumbering. Careerism, ideology, personality, friendships, and tribal loyalties also have a large role. I have even seen politicians do the right thing for no other reason than it being the right thing.