Are the secret factions based on the real world?
In The Secret World, there are three primary factions that feel as though they are meant to be based in reality: the Illuminati, the Templars, and the Dragon.
The Illuminati seems obvious. It's based on the real-world conspiracies of a secret organization that controls American politics, banks, and media. But because they are so "known" to us, that makes me assume that the other factions are meant to be known, as well. But I can't quite put my finger on it.
What exactly are the Templars? Knights? Crusaders? The game implies this is a faction that lives on to this day, but to my knowledge, they would have been long dead. There's even strong implication that the Illuminati and Templars once coexisted in Europe prior to the colonization of America.
What exactly is the Dragon? Yakuza? Triads? The game makes it clear that this is an Asian organization, but also attaches strong implications of mysticism which makes me wonder if they are based in reality, at all.
What "real-world" factions are the Templars and the Dragon based on? Are these fictional factions mostly real-world or mostly fantasy?
Also, if your evidence is spoiler-ridden, please refrain from including it. I will take your assertions as though they have evidence!
Solution 1:
It would seem that the factions are loosely based on the real world.
As you suspected Illuminati are perhaps the best known - Wikipedia.
As two bugs mentioned, Templars are related to the Knights Templar, as seen on the wiki. The idea being that we wouldn't know if the original faction lived because it is a secret society.
The Knights Templar are basically a radical separatist group of The Secret World's Templars
Source
However, there are some entirely fictional elements
Ragnar: Templars aren't about Christianity. They're about Faith. Which is different. And also about kicking demon ass. —Ragnar Tørnquist, Twitter Interview
The Dragon are a little less defined, likely because they are meant to be the most secretive. They do have some specific inspirations. Without spoilers there are some specific events with China they are officially tied to. While they may be related to the Triads or Yakuza (as Templars to Knights Templar) they are not currently based in these countries. Although it is stated that they have changed locations multiple times, some other organizations may be a better fit. Following this, we should look at China, Korea, and Japan. As speculation I would say that they were (within the game history) the Black Dragon Society (in Japan), which was destroyed at the end of world war 2.
This would be supported by
They reformed in Seoul sometime after the Second World War, which marked the end of the previous Dragon generation.
Source
For a final speculation, I would say the closest current tie would be the Double Dragon Gang. It is close in location and name to the Dragon society, and had recently gone underground prior to the game's release.