Unfortunately your question uses very broad terms. Why exactly is Pagan type worship? Animal sacrifices? Worship of multiple gods? Worship of the Sun? Worship of nature? And this has various contradictions, Greco-Roman paganism seems to condone dominating nature and bringing man made order to to chaos of nature, while Celtic paganism is more pro-nature.
Also, what exactly are "Illuminati groups?" The Bavarian Illuminati? The Knights Templar? The Free Masons?
Ultimately, by what I think you mean by Illuminati groups, they mostly fall under Protestant or Atheistic ideologies. The Bavarian Illuminati were mostly the big money of Europe during industrialization. Bankers, Business owners, rich merchants. Basically these people didn't want a Church telling them they had obligation to feed the poor or give good wages. They were more likely atheists than anything else. But historians dont really have a lot of reliable information on the Bavarian Illuminati, and the group is greatly exaggerated.
The Free Masons had very orthodox protestant ideologies. They were advocates of the famed Protestant work ethics and no reliable information about them makes them anything other than good Christians.
Actually I would argue that the biggest rise of Pagan ideologies came in the Italian Renaissance within the confines of the Catholic Church. I wont say Pagan worship, but Pagan ideology. Classical Pagan authors were widely read, Pagan sciences and logic's were rediscovered. Pagan humanism was Incorporated into the Catholic Church.
So I would argue that the truth is the exact opposite of what you claim. However, modern literature and media likes to find similarities and links between these "Illuminati groups" and paganism, but unfortunately their really isn't any historical evidence to support many of these links. Think the Da Vinci Code, they make a link between the Templar's, the Merovingian Kings, and ancient Paganism, but their really isn't any historical evidence for this. I will admit, it SEEMS like their is a link, but thats just the Media and Pop Culture, not history. But it makes a good story.