I've never quite understood the Satanic allegation. The Illuminati are often mistaken for the Free Masons. Masonic symbolism and religion is borrowed from ancient traditions, they use Egyptian, Greek, and other ancient symbols. Masonic beliefs tend to be deistic but they get a bad reputation for their use of so-called "Occult" symbols.
As for the Illuminati it's unclear if they even exist in any form these days, other than in the minds of conspiracy theorists. Whether they are Satanic or not remains to be seen but most people believe they are made up of rich and powerful businessmen, politicians, athletes and musical artists/actors. If the powerful worship any god at all it's likely to be money, not some fallen angel from ancient mythology. Though if they ARE like the Masons than who knows what traditions they borrow from for their rites.