Same reason some Protestants also teach that the Jesuits are involved in bizarre conspiracy theories.
It is true that a real Illuminati existed in the 18th century, but it rapidly declined and pretty much disappeared off the face of the earth. Subsequently, conspiracy theories started floating around that they were responsible for the French Revolution, but it’s just that: a conspiracy theory, with no substantial evidence to back it up.
In short, to answer your question: no, there’s no substantial evidence that shows an “Illuminati” secret society is in charge of major world events, it is just a conspiracy theory.