Well, Vatican City is a theocracy ruled by the pope; leader of the Catholic Church. So the link is pretty clear there. As for the Illuminati, they were a Bavarian secret society founded in 1776 that sought to oppose the clergy and the monarchy. You would imagine the Catholic Church would vehemently oppose them, and you would be right... if they still existed, at least. The society didn't last more than a few years: the thing about secrets is that they don't like being secret for too long. Case in point, their existence had become well known to the public and the king was understandably a bit upset. Thus, all secret societies were banned, effectively killing the Illuminati. I say "effectively" because the thing was already going downhill due to all sorts of drama between members. I do recommend everyone to do some research on the truth (the actual truth) of these matters, because they show how easily these sorts of schemes fall apart. It's not easy to keep secrets. It's not easy to manage an organization. It's not easy to dismantle regimes and infiltrate powerful institutions. And it's definitely not easy to do all these things at once and at a global scale.