The Founding Fathers were generally speaking....non-religious...especially, Thomas Jefferson and James Madison.

Both Jefferson and Madison were Deists-(which, at the time, was a very popular intellectual movement during the greater Enlightenment era). It was Thomas Jefferson, who penned the phrase..."Nature's God", when introducing The Declaration of Independence; and it was James Madison who was largely credited for having established....."The Establishment Clause", which serves as the opening/introductory language to the greater Bill of Rights.

While Jeffersonian Deism is historically significant, it was not legalistically worded, whereas Madisonian Deism, was legalistic in tone and has served as the Constitutional basis for religious liberty-(and in a way, has also served as the basis for religious libertarianism), for over 230 consecutive years.

"Nature's God", as well as the word, "Creator" appear in The Declaration of Independence, though there is no explicit referencing to God, nor is there any explicit referencing to Jesus or Christianity....the same can also be said for The First Amendment, however the word, "religion" does appear in The Establishment Clause.

The phenomenon of an American President's Christian faith seems to be more rooted in Contemporary U.S. History, beginning with Ronald Reagan and years later with, George W. Bush Junior. This is not to say that the 200 plus year history of The American Presidency was completely estranged from Christianity. However, the political and public vocalization of an American President's Christian faith appears to be more contemporarily rooted and is not necessarily rooted in the identities and policies of earlier U.S. Presidents-(perhaps with the exception of John F. Kennedy and his Catholic faith).

Question:
Has the United States ever had a non-Christian President?

Short Answer:

Roughly 18% - 25% of all American Presidents were "non- Christian". Or stated another way, arguable the United States did not have a Christian President until the eighth: President Martin Van Buren, who was Dutch reform. I say arguable because three Presidents overall, and two in the first 7, are questionable: George Washington, Andrew Jackson, and James Madison, whose religious affiliations when President are argued by historians.

All Told the Presidential breakdown is…

• 33 Protestants
• 4 Nontrinitarian Deists – George Washington?, Jefferson, James Madison(?), James Monroe
• 4 Nontrinitarian Unitarians – John Adams, John Q Adams, Milard Filmore, William Howard Taft
• 3 Not specified – Lincoln, Andrew Johnson, Andrew Jackson(?)
• 1 Roman Catholic – Kennedy

Terms:

To answer this question, one must define what being a Christian means.
For our purposes, we will define "Christian" broadly as those who believe in the divinity of Christ. If you believe Christ was a prophet from god as the Muslims do for our purposes, we won't consider you a Christian. If you believe he was a smart moral leader with good ideas which you subscribe too, but don't worship him as god, then for our purposes that's not Christian. We will also include those persons who were not religious in office and never claimed any religious affiliation as non-Christians.

It is important to define the terms because being a non Christian historically has carried with it a stigma which politicians would be eager to avoid. Many politicians who do not fit our simple boundaries, have claimed the designation Christian, while denying the divinity of Christ. Presidents like Thomas Jefferson, who was a Deist, would refer to himself as Christian but always with caveats. As Jefferson said that he was "Christian in the only sense in which he (Jesus) wished any one to be", which side stepped the issue that Jefferson didn't believe in Christ as the son of God, miracles, or even that Jesus was influenced by God.

(President Jefferson to Benjamin Rush) 1803 April 21.
I am a Christian, in the only sense in which he wished any one to be; sincerely attached to his doctrines, in preference to all others; ascribing to himself every human excellence, & believing he never claimed any other."

(Jefferson to Charles Thomson) 1816 January 9.
I am a real Christian, that is to say, a disciple of the doctrines of Jesus, very different from the Platonists, who call me infidel, and themselves Christians and preachers of the gospel, while they draw all their characteristic dogmas from what it’s Author never said nor saw.

(Jefferson to Timothy Pickering) 1821 February 27
[N]o one sees with greater pleasure than myself the progress of reason in it’s advances towards rational Christianity. when we shall have done away the incomprehensible jargon of the Trinitarian arithmetic, that three are one, and one is three; when we shall have knocked down the artificial scaffolding, reared to mask from view the simple structure of Jesus, when, in short, we shall have unlearned every thing which has been taught since his day, and got back to the pure and simple doctrines he inculcated, we shall then be truly and worthily his disciples

Jefferson believed Jesus had good ideas and was looking to influence people; from Jefferson's perspective, since he read the bible and was influenced he could thus claim the affiliation. Jefferson believed in God, but didn't believe God ever interacted with humanity.

Other founding fathers who declared themselves to be Christian but who do not our broad definition are John Adams and Millard Fillmore. John Adams was a Unitarian whose religious beliefs are well known to us, and he referred to himself as a Christian while professing the divinity of Christ as a "terrible blasphemy". Then you had Presidents like Millard Fillmore who was a Unitarian and a founding member of a Unitarian congregation, affiliated for three decades, but still denied his affiliation with Unitarianism when approached by other Unitarians. Presidents like William Howard Taft, who was openly Unitarian, have been more the exception.

Detailed Answer:

8 to 11 of 44(-) Presidents through Donald Trump either had unknown(3) religious affiliation, or not believed to have been Christians ( Deists(4), Unitarians(4)).

(-) see footnotes

Deists, some of which value Christian teachings and morals, believe in a Spinoza type Nature God, disinterested in human experience. They do not believe in the divinity of Jesus. They do not believe God has ever communicated with human kind directly or indirectly. Deists were the 18th century equivalent of Atheists or Agnostics. Prior to Darwin in the mid 19th Century, there was no explanation for the existence of humanity other than god. Deists thus attributed the creation of humanity and the universe to god, but a god who then checked out and left humanity to its own fate. A god who never interacted nor was interested in humanity.

Deism
belief in the existence of a supreme being, specifically of a creator who does not intervene in the universe. The term is used chiefly of an intellectual movement of the 17th and 18th centuries that accepted the existence of a creator on the basis of reason but rejected belief in a supernatural deity who interacts with humankind.

Unitarians also believe in God, but not the trinity. Unitarians also may value the social order and moral teachings of Christianity, while not subscribing divine motivations to those teachings. The name Unitarian is coined from their rejection of the trinity(three god heads), as they believe in 1 god head the father. Jesus is not a God Head for Unitarians. Unitarians refer to their beliefs as supporting "Christology", the moral teachings of Christ, rather than to themselves as "Christians". They do not believe Jesus was the son of God in the sense that he was unique, nor do they believe he was raised from the dead, nor sent by god, nor that he died for all men, nor that he meant to create a religion called Christianity, a new covenant with men.

Unitarians believe in the moral authority but not necessarily the divinity of Jesus. Their theology is thus opposed to the trinitarian theology of other Christian denominations.

Unitarian Christology can be divided according to whether or not Jesus is believed to have had a pre-human existence. Both forms maintain that God is one being and one "person" and that Jesus is the (or a) Son of God, but generally not God himself.

In the early 19th century, Unitarian Robert Wallace identified three particular classes of Unitarian doctrines in history:

• Arian, which believed in a pre-existence of the Logos, but maintained that Jesus was created and lived as human only;
• Socinian, which denied his original divinity, but agreed that Christ should be worshipped; and
• "Strict Unitarian", which, believing in an "incommunicable divinity of God", denied both the existence of the Holy Spirit and the worship of "the man Christ."

As previously mentioned, Jefferson a non-trinitarian/deist who converted in his youth while studying at William and Mary, the center for deist teachings in colonial Virginia.

The Religion of James Monroe
In Virginia, the center of Deism was Monroe and Jefferson’s alma mater, the College of William and Mary in Williamsburg, an institution where Washington also served as chancellor. “At the end of the century,” Bishop William Meade of Virginia, an orthodox Episcopalian, remembered in his Old Churches, Ministers and Families of Virginia, “the College of William and Mary was regarded as the hotbed of infidelity and of the wild politics of France”:

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The Breakdown

• 33 Protestants
• 1 Roman Catholic – Kennedy

  • 4 Nontrinitarian Deists – George Washington?, Jefferson, James Madison(?), James Monroe
  • 4 Nontrinitarian Unitarians – John Adams, John Q Adams, Milard Filmore, William Howard Taft
  • 3 Not specified – Lincoln, Andrew Johnson, Andrew Jackson(?)

Arguable 11 non-christian presidents.

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The Question marks

1. George Washington

Even during his lifetime, people were unsure about the degree to which Washington believed in Christianity. As noted above, some of his contemporaries called him a deist. Debate continues to this day regarding whether he is best categorized as a deist or as a Christian, and some writers have introduced other terms to describe a blending of the two.

2. Andrew Jackson who was a Presbyterian, but only joined the Presbyterians after his presidency. So technically his religion as President was unknown.

   Andrew Jackson was brought up in a Presbyterian family. Although he had little interest in religion early on, Jackson became increasingly religious, eventually joining the Presbyterian church in 1838. ( left office in 1837 ).

3. James Madison was a low key Episcopal, but his writings represent his religious beliefs to be those of his mentor and great friend Thomas Jefferson, that is: deism.

   Considered to have been a deist, James Madison, late in life, wrote, “Belief in a God All Powerful wise and good is so essential to the moral order of the World and to the happiness of man, that arguments which enforce it cannot be drawn from too many sources.”

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Deists

4. Thomas Jefferson
   quotes previously provided.

5. James Monroe’s

   Yet over the years James Monroe’s biographers have rarely mentioned his religious views. Even those who have written books on the religion of the American presidents have found little to say when they have reached the religion of the fifth president of the United States. There is a reason for this dearth of material, and it is called Deism.

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The Unitarians

6. John Adams

John Adams’s biographer and the editor of his Works, his grandson Charles Francis Adams, wrote that “with the independent spirit which in early life had driven him from the ministry, [Adams rejected] the prominent doctrines of Calvinism, the trinity, the atonement and election. . . .”
.
Moreover, church-state scholar Greg Hamilton says John Adams criticized the notion of Christ’s divinity as an “awful blasphemy.”

7. John Quincy Adams

   He became one of the 27 founding members of the First Unitarian Church of Washington. His acceptance of the Unitarian name by no means signaled an abrupt change in his thinking, for he had for a long time evidenced liberal leanings. His acceptance of the professorship at Harvard was made on condition that the usual requirement for a declaration of religious conformity be waived; moreover, his deep interest in the study of theology and the Bible, despite the uncertainties that went with this, indicates that, in the best Unitarian tradition, he was a dedicated seeker after religious truth.

8. Millard Filmore

   Fillmore had liberal ideas about religion. He had been raised by nominal Methodists, studied under a Quaker judge, and may have attended or visited a short-lived Unitarian society in Kelloggsville. In late 1831 a Unitarian church was organized near the Fillmores' home in Buffalo. Millard became a charter member. Abigail, who had been brought up Baptist, did not actively participate.
   Fillmore's association with First Unitarian Church of Buffalo lasted for 35 years. He took John Quincy Adams to church with him there in 1843 and President-elect Abraham Lincoln in 1861. A letter written in 1849, turning down an invitation to speak at a Unitarian meeting in Boston, saying, "I sympathize with those who inhance liberal Christianity. But yet I am not a member of the Unitarian church," remains puzzling. He had contributed much money to the Unitarian church, including a registered payment in 1848.

9. William Howard Taft
   The sole Unitarian President since Millard Fillmore, he remains the only Unitarian Chief Justice. He is remembered for services to his fellow religious liberals and to the American Unitarian Association.

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Un-Affiliated

10. Andrew Johnson

Johnson belonged to no church and was not much of a church-goer. Although he was quite tolerant of religion and religious belief, Johnson showed little personal interest in religion.

11. Abraham Lincoln

William Herndon, Lincoln's law partner, stated that Lincoln admired deists Thomas Paine and Voltaire. Herndon, an advocate of Darwin's, said Lincoln thought the works of authors like Darwin and Spencer "entirely too heavy for an ordinary mind to digest" but he read and was "interested ... greatly" in a book expounding on these ideas, "Vestiges of Creation", and he was "deeply impressed with the notion of the so-called 'universal law' — evolution... and he became a warm advocate of the new doctrine."

Lincoln believed in God, but some said he doubted the idea that Christ is God. In a written statement to Herndon, James W. Keyes said Lincoln

believed in a Creator of all things, who had neither beginning nor end, who possessing all power and wisdom, established a principal, in Obedience to which, Worlds move and are upheld, and animel and vegatable life came into existence. A reason he gave for his belief was, that in view of the Order and harmony of nature which all beheld, it would have been More miraculouis to have Come about by chance, than to have been created and arranged by some great thinking power.[27]

Keyes also added that Lincoln once said

As to the christian theory, that, Christ is God, or equal to the Creator he said had better be taken for granted — for by the test of reason all might become infidels on that subject, for evidence of Christs divinity Came to us in somewhat doubtful Shape — but that the Sistom of Christianity was an ingenious one at least — and perhaps was Calculated to do good.

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Footnote

(-) Trump is said to be the 45th President because people count Grover Cleveland twice (22, and 24th Presidents). For our purposes of calculating percentage of non-christian presidents, there were only 44 people who have occupied the office of the Presidency from Washington to Trump. We don't need to count Cleveland in our calculation twice.

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Jefferson Quotes

• 1787 August 10. (Jefferson to Peter Carr). "Fix reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a god; because, if there be one, he must more approve the homage of reason, than that of blindfolded fear."
• 1803 April 21. (Jefferson to Benjamin Rush). "[T]o the corruptions of Christianity, I am indeed opposed; but not to the genuine precepts of Jesus himself. I am a Christian, in the only sense in which he wished any one to be; sincerely attached to his doctrines, in preference to all others; ascribing to himself every human excellence, & believing he never claimed any other."
• 1814 September 26. (Jefferson to Miles King). "I must ever believe that religion substantially good which produces an honest life, and we have been authorised by one, whom you and I equally respect, to judge of the tree by it's fruit. our particular principles of religion are a subject of accountability to our god alone. I enquire after no man's, and trouble none with mine: nor is it given to us in this life to know whether your's or mine, our friend's or our foe's are exactly the right."
• 1816 January 9. (Jefferson to Charles Thomson). "I too have made a wee little book, from the same materials, which I call the Philosophy of Jesus. it is a paradigma of his doctrines, made by cutting the texts out of the book, and arranging them on the pages of a blank book, in a certain order of time or subject. a more beautiful or precious morsel of ethics I have never seen. it is a document in proof that I am a real Christian, that is to say, a disciple of the doctrines of Jesus, very different from the Platonists, who call me infidel, and themselves Christians and preachers of the gospel, while they draw all their characteristic dogmas from what it’s Author never said nor saw. they have compounded from the heathen mysteries a system beyond the comprehension of man, of which the great reformer of the vicious ethics and deism of the Jews, were he to return on earth, would not recognise one feature. if I had time I would add to my little book the Greek, Latin and French texts, in columns side by side, and I wish I could subjoin a translation of Gassendi’s Syntagma of the doctrines of Epicurus, which, notwithstanding the calumnies of the Stoics, and caricatures of Cicero, is the most rational system remaining of the philosophy of the ancients, as frugal of vicious indulgence, and fruitful of virtue as the hyperbolical extravagancies of his rival sects."
• 1821 February 27. (Jefferson to Timothy Pickering). "[N]o one sees with greater pleasure than myself the progress of reason in it’s advances towards rational Christianity. when we shall have done away the incomprehensible jargon of the Trinitarian arithmetic, that three are one, and one is three; when we shall have knocked down the artificial scaffolding, reared to mask from view the simple structure of Jesus, when, in short, we shall have unlearned every thing which has been taught since his day, and got back to the pure and simple doctrines he inculcated, we shall then be truly and worthily his disciples: and my opinion is that if nothing had ever been added to what flowed purely from his lips, the whole world would at this day have been Christian. I know that the case you cite, of Dr Drake, has been a common one. the religion-builders have so distorted and deformed the doctrines of Jesus, so muffled them in mysticisms, fancies and falsehoods, have caricatured them into forms so monstrous and inconcievable, as to shock reasonable thinkers, to revolt them against the whole, and drive them rashly to pronounce it’s founder an imposter. had there never been a Commentator, there never would have been an infidel. in the present advance of truth, which we both approve, I do not know that you and I may think alike on all points. as the Creator has made no two faces alike, so no two minds, and probably no two creeds. we well know that among Unitarians themselves there are strong shades of difference, as between Doctors Price and Priestley for example. so there may be peculiarities in your creed and in mine. they are honestly formed without doubt. I do not wish to trouble the world with mine, nor to be troubled for them. these accounts are to be settled only with him who made us; and to him we leave it, with charity for all others, of whom also he is the only rightful and competent judge. I have little doubt that the whole of our country will soon be rallied to the Unity of the Creator, and, I hope, to the pure doctrines of Jesus also.