Jefferson on the Freemasons:

Thomas Jefferson was not a Freemason (as some mistakenly believe). Though he had no problem with them and in the following letter to Bishop James Madison (cousin to the Founding Father of the same name), praised an "Illuminated" Mason named Adam Weishaupt (see number 8 in the below link) (hat tip Tom Van Dyke):

Barruel’s own parts of the book are perfectly the ravings of a Bedlamite. But he quotes largely from Wishaupt whom he considers as the founder of what he calls the order. As you may not have had an opportunity of forming a judgment of this cry of 'mad dog' which has been raised against his doctrines, I will give you the idea I have formed from only an hour’s reading of Barruel’s quotations from him, which you may be sure are not the most favorable. Wishaupt seems to be an enthusiastic Philanthropist.

He is among those (as you know the excellent Price and Priestley also are) who believe in the indefinite perfectibility of man.

Indeed, Jefferson saw in such Freemasons folks who preached the same kind of religious principles in which he believed. He even compared "Wishaupt" to his spiritual mentor, Joseph Priestly, and Richard Price, another British unitarian who strongly influenced Jefferson and America's key Whig Founders. Note, they believed "in the indefinite perfectibility of man," which is not consistent with orthodox Christianity because it denies original sin. Neither is Locke's notion of a tabla rasa or "blank state" for human nature (or at least for the human mind).

Jefferson continues on "Wishaupt":

Wishaupt believes that to promote this perfection of the human character was the object of Jesus Christ. That his intention was simply to reinstate natural religion, & by diffusing the light of his morality, to teach us to govern ourselves. His precepts are the love of god & love of our neighbor. And by teaching innocence of conduct, he expected to place men in their natural state of liberty & equality. He says, no one ever laid a surer foundation for liberty than our grand master, Jesus of Nazareth. He believes the Free Masons were originally possessed of the true principles & objects of Christianity, & have still preserved some of them by tradition, but much disfigured.

Though I've never read Adam Weishaupt's work, this is exactly what Jefferson, after Joseph Priestly, believed about Jesus and Christianity freed from its "corruptions" (i.e., the tenets of orthodoxy that distinguish it). Jesus was a man, not God, and a great moral teacher who preached "natural religion," -- a sort of universalistic ethical monotheism that man can discover from reason.

This also shows that when Madison, for instance, referred to Christianity as the "best & purest religion," it by no means pointed towards his belief in orthodox Christianity as such contention perfectly parallels Jefferson's above quoted heterodox thoughts. This is why James H. Hutson noted about that quotation:

This last assertion, however, sounds very much like the deistical maxim, frequently indulged by Jefferson, that the "pure" religion of Jesus had been unconscionably corrupted by the apostle Paul and the early church fathers.

Jefferson continues on Weishaupt:

The means he proposes to effect this improvement of human nature are 'to enlighten men, to correct their morals & inspire them with benevolence. Secure of our success, sais he, we abstain from violent commotions. To have foreseen the happiness of posterity & to have prepared it by irreproachable means, suffices for our felicity. The tranquility of our consciences is not troubled by the reproach of aiming at the ruin or overthrow of states or thrones.'

As Wishaupt lived under the tyranny of a despot & priests, he knew that caution was necessary even in spreading information, & the principles of pure morality. He proposed therefore to lead the Free masons to adopt this object & to make the objects of their institution the diffusion of science & virtue. He proposed to initiate new members into his body by gradations proportioned to his fears of the thunderbolts of tyranny.

This has given an air of mystery to his views, was the foundation of his banishment, the subversion of the masonic order, & is the colour for the ravings against him of Robinson, Barruel & Morse, whose real fears are that the craft would be endangered by the spreading of information, reason, & natural morality among men.

It's a wonder why Jefferson never joined the Freemasons as he saw them as teaching exactly what he believed in.