As I understand it, Kristo's historical definition of Christianity differs not much from Paul Sigmund's, professor of politics at Princeton, whom I've met personally and briefly discussed this issue (I work near Princeton and attend Prof. Robert George's James Madison Program lectures when time permits; though I disagree with Dr. George on social issues, his program does outstanding research on America's Founding).
Dr. Sigmund, as far as I know, a political and liberal Christian, defines a "Christian" (reasonably, I think) as someone who believes Jesus a "Savior" or Messiah in some kind of divinely special way. As such, along with Trinitarians, Socinians (who believe Jesus 100% man, not God at all, but who saved man through his perfect moral example) and Arians (who believe Jesus a divine savior, but created by and subordinate to God the Father) qualify as "Christians" as do Mormons, Jehovah's Witnesses, and others. As such, one arguably could term Jefferson, Franklin, J. Adams and almost all of the "key Founders" and ministers and philosophers they followed as "Christians" regardless of their particular beliefs on matters such as original sin, trinity, incarnation, atonement, eternal damnation, and infallibility of the Bible. (That is, this definition of Christianity excludes Thomas Paine, Ethan Allen, Elihu Palmer, but not Jefferson, Franklin, J. Adams, Madison, Washington etc.)
The day I questioned Dr. Sigmund at Princeton, I also spoke to Dr. Jeffry Morrison of Regent University who presented on his book on George Washington's political philosophy and Morrison made clear he thought one must be an orthodox Trinitarian to qualify as a "Christian." (Hence his book concludes that though GW was influenced by "Christianity" he could not conclude that GW was a "Christian").
My biggest issue with Kristo is that he doesn't see (as I do) that when David Barton lectures mainly to evangelical audiences and promotes the "Christianity" of America's Founders and how it helped shape America's political institutions, they (Barton's audience) hear orthodox Trinitarianism, the Bible as the inerrant infallible Word of God, and who knows what else (being born again?), when Barton uses terms like "Christian" or "Christianity."
So I was happy to dialog, via email, with an evangelical minister, smart, prominent, sympathetic to David Barton and the "reclaiming" of America on behalf of "Christianity" cause, to "test" the Christian Nation thesis, as it were. This is what I asked him:
[W]hat do you call someone who calls himself a "Christian," but disbelieves in original sin, trinity, incarnation, atonement, eternal damnation? Someone who may even believe Jesus a "Savior" of mankind (thru his perfect moral example) perhaps even a divine Savior created by but subordinate to God the Father (not 2nd person in the Trinity). Someone who believes in an active Providence and that parts, perhaps the majority of the Bible are revealed by God, but that the Bible is not inerrant or infallible.
And what follows is his answer (which he gave me permission to reproduce):
I do not believe you can truly be a Christian and hold several of the positions you state below.
1. The Bible clearly teaches ‘original sin’ as you call it, and that it was passed on to all mankind; that we are all sinners and in need of salvation, and that it is through the shedding of Christ’s blood that our sins are atoned for and forgiven. It is when a person personally and honestly acknowledges that he has a sin problem and is therefore a sinner, and sincerely, truly, and humbly places his faith in Christ as Who He claimed to be, The Son of God, and asks forgiveness of his sins, is he saved, or, born again. It is not merely ‘intellectual assent’ to the ‘possibility’ that He was God, or might be, or was the greatest human being that ever lived. It is a recognition, from the heart and in your spirit, that you are a sinner, no matter how much you want to rationalize it, or get around it, or kid yourself. It is coming honestly and openly before God, and your inner man, not your public man, and yielding, surrendering to God Who was in Christ, that you become a Christian, and that what the Bible says about Christ, sin, and man, is true and that he therefore is LORD of all.
2. You cannot, if you are a student of the Word, and believe what Christ said, and said about the Scriptures, ‘disbelieve in original sin, the trinity, incarnation, atonement, and eternal damnation,’ and still call yourself a Christian because a sincere and true Christian knows that all those things are part and parcel of what Christ taught. You would be denying the very teaching of Christ, and …therefore…you are your own god, and not a true believer, and…are probably more than just confused. You are most likely not even a Christian because you do not honor Him or His Word.
3. “Someone who may even believe Jesus a "Savior" of mankind (thru his perfect moral example – which is impossible) perhaps even a divine Savior created by but subordinate to God the Father (not 2nd person in the Trinity)” is not a Christian, because that is not what Christ taught nor does the O.T. support. [Emphasis in the original.]
4. “Someone who believes in an active Providence and that parts, perhaps the majority of the Bible are revealed by God, but that the Bible is not inerrant or infallible” may call themselves a Christian, but they are certainly not a skilled student of the Bible. Sounds like Jefferson to me.
In my opinion, the Rev.'s answer illustrates the mindset, not necessarily of the ordinary people in evangelical churches who hear Barton's message, who are not as intelligent and spiritually discerned, but of the learned, ministerial types.
But it's clear that according to the understanding of "Christianity" of the churches to whom Barton sells his message, he tries to pass off Founders and ministers from that era as "Christian" who flunk the test of said churches.
Here is exhibit A against Barton in this regard. He rattles off names -- John Adams' list of those most responsible for American Independence: Samuel Cooper, Jonathan Mayhew, Charles Chauncy, and George Whitefield. He calls them all ministers of the gospel and all Christians.
In reality ONLY WHITEFIELD was a "Christian" as evangelicals define and understand the term. The others, including J. Adams were Trinity deniers. But when evangelicals and other "orthodox Christians" hear David Barton rattle off these names and term them "Christians," what do they think?!?
Finally let me note that one could lower the "test" for Christianity one or a few steps than the tight evangelical test (that might include things such as salvation thru grace alone, being "born again") as Dr. Gregg Frazer does in his 10 point test which takes a lowest common denominator among creeds of the largest churches in late 18th Century America (that includes Roman Catholicism). But America's key Founders and the notable patriotic preachers they followed (Revs. Mayhew, Chauncy, Cooper and others) disbelieved in central Christian tenets like original sin, trinity, incarnation, and atonement, such that they are disqualified as "Christians" in the eyes of large sectors of believers in historic traditional Christianity.