Why is this important? David Barton and the other Christian Nationalists are sympathetic to the notion that the organic law of the United States is "Christianity generally." Well that begs the question, what is Christianity? To most evangelicals, Roman Catholics and capital O Orthodox Christians, Christianity is synonymous with orthodoxy (Christ's divine nature as God the Son, second person in the Trinity, the Atonement, etc.) A theological system that rejects these tenets is "not Christianity" whatever it calls itself.
Well, it would follow then, if Washington intended to establish "Christianity generally" -- which defines as orthodox Trinitarian doctrines under which the different Christian sects were united -- as the "civil religion" of America, his public God talk would often be done in the name of the "Father, Son, and Holy Spirit," the infallibility of the Bible and would cite verses and chapters of scripture as "trumping" authority.
But Washington's public God talk [for instance the content of Washington's first Thanksgiving Proclamation] does none of this. Now, it could be that Washington was an orthodox Trinitarian Christian, privately, but publicly didn't want that specific form of Christianity to be the "de facto" civil religion and avoided mentioning these doctrines to make America seem more inclusive and welcoming of diverse faiths. Certainly Presidents who have been orthodox in their personal theology like Jimmy Carter or George Bush opt for this message of public inclusive God talk while remaining privately orthodox.
However, if Washington were privately orthodox, we would expect to see his private writings, especially communication with orthodox figures, peppered with orthodox Trinitarian theology, but we don't. Indeed Brad Hart uses Peter Lillback's research against his thesis that Washington was an orthodox Trinitarian Christian. Lillback has two theses, one -- that Washington wasn't a Deist (which he proves) -- and two -- that Washington was orthodox (which he doesn't). Drawing from Lillback's research, Hart reproduces "the actual phrases that Washington used in his 'written prayers' to describe divinity, along with the number of times they were used:"
"Providence" - 26 times
"Heaven" -25 times
"God" - 16 times
"Almighty God" - 8 times
"Lord" - 5 times
"Almighty" - 5 times
"Author of all Blessings" - 3 times
"Author of the Universe" - 3 times
"God of Armies" - 3 times
"Giver of Victory" - 3 times
"Great Ruler of the Universe" - 2 times
"Divine Protector" - 2 times
"Ruler of Nations" - 2 times
"Particular Favor of Heaven" - 2 times
"Divine Author of Life and Felicity" - 2 times
"Author of Nations" - 1 time
"Divine Being" - 1 time
"Allwise Dispenser of Human Blessings" - 1 time
"Supreme giver of all good Gifts" - 1 time
"Sovereign Dispenser of Life and Health" - 1 time
"Source and Benevolent Bestower of all good" - 1 time
"Power which has Sustained American arms" - 1 time
"Allwise Providence" - 1 time
"Infinite Wisdom" - 1 time
"Eye of Omnipotence" - 1 time
"Divine Author of our Blessed Religion" - 1 time
"Omnipotent being" - 1 time
"Great Spirit" - 1 time
"Glorious being" - 1 time
"Supreme being" - 1 time
"Almighty being" - 1 time
"Creator" - 1 time
"Jesus Christ" - 0
"Salvation" - 0
"Messiah" - 0
"Savior" - 0
"Redeemer" - 0
"Jehovah" - 0
Not once is Washington recorded as praying "in Jesus' name." This is why Christian Nationalists are so desperate to use Washington's spurious "Daily Sacrifice" prayerbook, because that contains orthodox theology.
The profound insight that Dr. Gregg Frazer posits in his PhD thesis is that the private theology of the key Founders [Washington, J. Adams, Jefferson, Madison, Franklin, etc.] was indeed the public civil religion which they established in their public God talk and was the ideological theology behind the Declaration of Independence and US Constitution.