Chapter 25 in George Washington's Sacred Fire. What's laudable about how Dr. Lillback deals with George Washington's membership in the Masonic Order is that he doesn't try to downplay it as some orthodox Christians do. Lillback recognizes that Washington was intimately involved with the Freemasons, though notes during the last 30 years of Washington's life, he didn't actively participate much, mainly because of time constraints; he was busy founding the nation and running the country.
Washington answered a letter by one GW Snyder
The fact is, I preside over none, nor have I been in one more than once or twice, within the last thirty years. I believe notwithstanding, that none of the Lodges in this Country are contaminated with the principles ascribed to the Society of the Illuminati. With respect I am &c.
GW Snyder, a Founding era version of a conspiracy nut, feared the Illuminati and their nefarious agenda.
Though he claimed to have infrequently attended lodges in the latter years of life, Washington was nonetheless intimately involved with the Masons. Indeed, he was a Master Mason who was buried with full Masonic rites and participated in the Masonic ceremony of laying the cornerstone at the capitol. Moreover, Washington never renounced his affiliation with the Masons and, as President, defended and approved of their organization while frequently corresponding with them. For instance, in 1792 he wrote:
While I beg your acceptance of my thanks for the "Book of Constitutions" you have sent me, and the honor you have done me in the dedication, permit me to assure you that I feel all those emotions of gratitude which your affectionate address & cordial wishes are calculated to inspire: and I sincerely pray that the Great Architect of the Universe may bless you and receive you hereafter into his immortal Temple.
Lillback's response is that the Masons at that time preached nothing inconsistent with orthodox Christianity. He notes there were "Christian Masons," of which Washington was one. And that some Masonic Christians of Washington's day actually forbade strict Deism. One such document, for instance, reads that Masons were not to "tread in the irreligious paths of the...Deist nor stupid Atheist." (p. 505)
As he does over and over in his book, Lillback raises up a strict Deist strawman. It wasn't the Deism that Masonry allegedly promoted which made it inconsistent with Christianity, but its syncretism or universalism. Freemasonry, even the so called "Christian" kind in which Washington was involved arose out of the zeitgeist of Enlightenment rationalism. And, it promoted the religion of rationalism -- natural religion. Deism, of course, is a species of natural religion. However, unitarianism and some versions of orthodox Christianity likewise incorporate natural religion. Natural religion is what reason, not scripture, reveals about God and the universe. For Christians, natural religion sees its fullest expression in the works of natural law philosophers Aquinas or Hooker.
Lillback quotes the founding era Presbyterian minister Samuel Miller explaining Freemasonry and natural religion:
Masonry, as such, and according to its original plan, appears to be founded on natural religion. Hence the institution is found among all nations, who believe in one God, and the accountableness of man to him, as a moral Agent, and an immortal being. (Ibid)
In other words, Masonry emphasises "reason" or natural religion and embraces all religions which believe in one God which would include Judaism, Islam, Christianity, Unitarianism, and Deism (even though some Christian Masons might not have approved of strict Deism). It's already starting to sound like what Gregg Frazer terms "theistic rationalism."
As far as its inconsistency with Deism, Thomas Paine was a Deist and a Freemason. But let's not make Deism a red herring. It's Freemasonry's universalism or syncretism which is relevant. Paine wrote that Freemasonry "transcends the bounds of Christian and Western civilization; it includes the Moslem, the Hindoo, the Buddhist, and the Jew."
So strong was the appeal of such syncretism or universalism that when the Founders "squinted" hard enough they could "find" monotheism, or the worship of one god in Hinduism or Pagan Greco-Roman worship. Indeed, Freemasonry may have influenced many non-Masons, for instance Jefferson and Adams, both of whose beliefs on all world religions worshipping the same one God perfectly paralleled the Masons'.
As noted, Freemasonry arose in an Enlightenment zeitgeist -- a subculture that the elite Whig Founding Founders were disproportionately members of, but the common man of the Founding era was not. Such "circles" or "associations" were the likely conduit for spreading ideas.
This website puts its finger on why Freemasonry, even the kind GW was involved with, is incompatible with orthodox Christianity (without getting into the conspiracy nonsense):
Freemasonry is incompatible with Christianity because it promotes indifferentism. Indifferentism is the heretical belief that all religions are equally legitimate attempts to explain the truth about God which, but for the truth of His existence, are unexplainable. Such a view makes all truths relative and holds that God can be equally pleased with truth and error. Because Christians believe that God has definitively revealed Himself in the person of Jesus Christ, and desires that all men come to the knowledge of this truth, indifferentism is incompatible with Christian faith. Jesus said, "I am the way, the truth, and the life; no one comes to the Father, but by me." (John 14:6).
Freemasonry's teachings and practices also result in syncretism which is the blending of different religious beliefs into a unified whole. This is evidenced most especially by Masonry's religious rituals which gather men of all faiths around a common altar, and place all religious writings along side the Bible on the Masonic altar. This is also demonstrated by the Lodge's prayers and its unique names and symbols for God and heaven. Syncretism is the logical consequence of indifferentism.
The Lodge's practice of requiring its members to swear immoral oaths is also incompatible with Christianity. These oaths require a Christian to swear on the Holy Bible that he will uphold a code of moral conduct that prefers Masons over non-Masons, and to preserve secret passwords and handshakes. Such oaths are gravely immoral because their subject matter is trivial or does not give rise to the necessity of an oath. These oaths are also sworn under symbolic, blood-curdling penalties of physical torture and death called self-curses (e.g., having my throat cut across, and my tongue torn out by its roots). These penalties show a lack of respect for God and amount to blasphemy which is a serious sin.
In other words, Freemasonry tries to be all things to all people. Now if one were both a Freemason and a member of an orthodox Christian Church, one would have to resolve the conflict by picking a side. And there probably were orthodox Christians, who were also Masons, and who believed in their orthodox Christian Church's teachings over Freemasonry's. (Apparently Parson Weems was a Freemason.) Yet, little if anything in the historical record indicates Washington was one such Christian.
In his public speeches and private writings, Washington was invariably "latitudinarian," used generic, philosophical terms for God, and promoted natural and enlightened religion. Like the Freemasons, he too tried to be all things to all people and systematically spoke to various individuals and groups in "their language." Indeed when he spoke to Native Americans who were uninterested in converting to Christianity, he referred to God as "The Great Spirit," exactly as they did (see here and here). Washington's words rarely if ever seemed to indicate he believed there was "just one way" to God, but the opposite.
Hence Washington's affiliation with the Freemasons and its impact on his thinking is just one more clue pointing in the direction of Washington's not being an orthodox Christian, but a theistic rationalist.