I'm speaking more in fictional terms, in terms of the conspiracy theory perception of Freemasonry, rather than trying to debate an actual philosophy of the organization.
So, in terms of conspiracy theory mythology, the Masons *do* resemble AC's Templars in a lot of ways. The conspiracy theorists have always linked Freemasonry directly to the real-life Knights Templar, and they supposedly share a lot of iconography. "New World Order," "Novus Ordo Seclorum," being the most famous example.
Not to mention war crimes and acts of terrorism openly, for centuries, against the indigenous population of their own country. Hence, why having a Native American protagonist might highlight quite a bit of that.