Weishaupt did not merely recruit freemasons, but high-level freemasons.
Still freemasons. If you want to abolish monarchical theocracy in favor of secular democracy, why not recruit the people that can have a real impact in that goal? I happen to agree with the stated goal of the Illuminati. Theocracy is a terrible thing to impose on a people.
As for as the Order of the Dragon, I guess that depends on why you think there are not conspiracy theories surrounding the Knights Hospitaller or the Teutonic Knights.
I didn't say the Knights Hospitaller, or the Teutonic Knights. The Knights Hospitaller was initiated in the 11th century in Jerusalem in order to protect a hospital, well before the Order of the Dragon, and continued well beyond, into the 18th century. The Order of the Dragon was initiated in Hungary by King Sigismund in the mid 15th century to fight the Ottoman Turks. It was popular in Germany, Italy, Wallachia, Serbia, and Hungary. The Teutonic Knights were initiated in Israel, but in the late 12th century, and were liquidated in the early 13th century for aligning themselves with the papacy, instead of the Hungarian crown. These three never even crossed paths. I've heard the conspiracies about the two you've mentioned, but crickets when it comes to the Order of the Dragon, outside of the stories of Vlad III.
Some groups are largely of fleeting significance, while others are not. What makes the Illuminati significant is the way it intertwined with European Freemasonry and its proximity to major world events like the French Revolution and Italian Unification. It also had a very clear and specific ideological agenda with regards to reshaping the world order at the time.
The Illuminati was permanently liquidated in 1785. Weishaupt wasn't the only man to dream of a world governed by secular democracy, either. It was a product of the Age of Enlightenment. Augustin Barruel started the conspiracy theory surrounding the Illuminati's involvement in the French revolution. He was also very much vested in the papacy, and was against the new French constitution. One of his scare tactics was the suggestion of an overthrow of Christianity, while he hid in England. I don't find this mans words to be trustworthy in the least, since he had more than enough motive and knowledge to scapegoat the Illuminati.
Is it possible that members of the forcibly disbanded group participated in the French revolution? Sure, but doubtful. Barruel was a very educated man, and every bit as vested in politics as he was the church. All it would have taken was Barruel coming into contact with publications of Weishaupt's appropriated writings. Weishaupt's beliefs stood in direct opposition to Barruel's ideology, which would make for a very convenient scapegoat. You can't prove who they are, where they are, or even how they were involved, but you could easily claim anyone to be involved if their removal proved convenient. The church itself used that very same tactic all throughout it's long, bloody history.
Comparing Freemasonry to a religion in terms of ideology is reasonable, but in terms of structure and function it is not even close to an accurate comparison
By modern religious standards, yes, it is different. That's because they use traditions of their past, and have a structural order based on skill sets when it was an organization of artisans and skilled workers. They wouldn't be the only religious group with structured tiers of membership, either. They resemble a very organized coven of pagan witches or, what would now be called, occultists.