Are certainly not modern Freemasons, no matter how much they claim to be. Well, Wikipedia says they were a "Catholic military order". So, let's figure out what that means, Wikipedia says it is a "Christian religious society of knights". Okay, good, though I think the source is about Canada, for whatever reason. But, how can one be a religious (here, meaning one who has taken certain vows) knight?
That actually isn't that hard to figure out. In 2 Timothy 2:3-4, Paul says (to Timothy)
"Take your share of suffering as a good soldier of Christ Jesus, No soldier on service gets entangled in civilian pursuits, since his aim is to satisfy the one that enlisted him".
That is what these knights were doing, they were trying to satisfy the one that enlisted them (they believed they had a call from God). They took Paul quite literally, here. They were literally soldiers for Christ.
Now, of course, there are a lot of myths about the crusades, and a book I recommend, is by Regine Pernoud, called "The Templars: Knights of Christ". I think people tend to forget that the whole reason people believe myths about The Templars, is that people are so willing to believe negative things about Catholics, that they believe the conspiracies along with them.
Some Templars WERE tried and executed for heresy. Mainly in France. Which had a king with financial problems. Who was a known opportunistic. The ironically named "Phillip the Fair" (Fillipe le bel).
I admit, this is not my area of expertise, so, I will probably write more when I get more information (and since I am on a Crusades kick at the moment, and also, I know enough French to read books in it, so, maybe I should do that). Now, I know that the Templars are not Freemasons for one very good reason: Masons aren't Catholic (although, some Catholics are Mason, in spite of it being condemned by the Church REPEATEDLY). Since I recommended a book, here's a podcast.
The Knights Templar - Jimmy Akin's Mysterious World
*Bible version used, Revised Standard Version, 2nd Catholic Edition.