I guess George Washington, freemason and our first president, was into said bullshit. Perhaps he was simply depressed and paranoid.
My understanding is that the origins of an Illuminati are distinct from the origins of Freemasonry. Generally, the Illuminati was borne in the late 1700s of a desire to upset the monarchical paradigm in favor of rule by those who possessed the strongest will to power and the most acute rational faculties. This agenda was transmuted for public consumption into the idea of an Age of Enlightenment (possibly the original New World Order). The Illuminati are also regarded as satanist or perhaps more accurately “Luciferian.” The idea is that Lucifer led a charge to liberate man from supplication to God by giving man God-like attributes. Also attributed as Illuminati “behavior” is concealment of evil in the appearance of good, so let’s say, for example that the Illuminati infiltrated the Catholic Church/Vatican and bent the agenda of the church towards satanism by masking their own will to power in “progressive” changes. So we get Vatican II which maybe switches “organic/healing” ritual with some kind of Illuminati-serving rituals and a green light on pedophilia to feed appetites upstream. This would be a hypothetical example. If there’s truth to the conflation of Illuminati and Freemasonry, the backstory is probably one of infiltration. Also, at the time of the Bavarian Illuminati in the late 1700s, apparently inidividuals were members of both societies.
I would suppose the “connection” in modern context is the perception that there are hidden hands at work in the creation of modern history. John F. Kennedy, another lonely, depressed and paranoid president openly decried the existence of secret societies in a democracy.
There is some psychological literature that talks about obsession with this information (more squarely “belief in conspiracies”) as a symptom of the need to assign a villain to an amoral tragedy. Speaking from personal experience, the obsession is simply a matter of the volume of information available. Imagine having to relearn everything you thought you already knew about politics, government, citizenship, the military, war, democracy, pop culture, history, food production, foreign policy, and so on—especially considering the morality/ethics of these missing stories are antithetical to the systems of belief and morality that you were raised with. Napolean said, “History is a set of lies agreed upon.” We learn about the crash of 1929 and Great Depression in American History, but we don’t learn that it was engineered by European bankers to get control of the money supply. That’s one of hundreds of examples.
The obsession begins with casually peeling back a wall on account of a few cockroaches and discovering thousands of them. How did this go unnoticed all this time?
Of course, one can know of these things broadly and not be obsessed, and I suppose the difference is that the established version of reality is somehow more pleasant or compelling or that the individual takes care to limit their focus to things they can directly influence.