Bishop William Meade was a pious Episcopalian Bishop of the founding era and a scholar who wrote a book [the entire thing has been digitized on google] Old Churches, Ministers, and Families of Virginia, where Meade gives valuable testimony on religion and America's founders. Meade was not entirely without his biases which sometimes cloud his work. He hoped, perhaps exercising wishful thinking, that as many of the founders as possible were real Christians like himself. Thus, when he testified that he didn't believe James Madison, for most of his adult life, was Christian, Meade makes such conclusions in spite of what his biases would otherwise lead him to conclude.
If I may summarize the entire passage in question before I reproduce it, he notes Madison may have flirted with orthodox Christianity at Princeton but right after coming back from college probably became something else, and remained something else until the very end of his life, perhaps converting to Christianity on his deathbed. Other than Meade's speculation on Madison's end of life conversion no evidence in the historical record shows Madison converted back to orthodox Christianity towards the end of his life.
The "something else" that Madison became was what I would call "theistic rationalism," or what David L. Holmes calls "moderate deism," or "Christian-Deism," and what James H. Hutson calls one of the many mansions of deism. It was not strict deism, however.
A few folks have alleged that Madison was a Christian when he wrote his Memorial and Remonstrance because of this particular passage in the document:
12. Because the policy of the Bill is adverse to the diffusion of the light of Christianity. The first wish of those who enjoy this precious gift ought to be that it may be imparted to the whole race of mankind. Compare the number of those who have as yet received it with the number still remaining under the dominion of false Religions; and how small is the former! Does the policy of the Bill tend to lessen the disproportion? No; it at once discourages those who are strangers to the light of revelation from coming into the Region of it; and countenances by example the nations who continue in darkness, in shutting out those who might convey it to them. Instead of Levelling as far as possible, every obstacle to the victorious progress of Truth, the Bill with an ignoble and unchristian timidity would circumscribe it with a wall of defence against the encroachments of error.
Two points in response. First, it's not clear that when Madison uses the word "Christianity," he means exclusively orthodox Trinitarian Christianity. Indeed even though most scholars are likely call theistic rationalism a type of "deism," the theistic rationalists were more likely to refer to themselves as Christians not deists. Indeed, I've blogged about notes Madison wrote preparing for the Remonstrance where he asks "what is Christianity?" and answers Christianity could be how the orthodox Churches have traditionally defined it, or a unitarian system (he mentions Arianism and Socinianism by name) that views the Bible as only partially inspired. In other words, theistic rationalism. Madison doesn't let us know which version of "Christianity" he endorsed. Though, most orthodox Christians of that era, like Meade for instance, were quick to label that system heresy or infidelity. He does make clear that he didn't want courts or any part of government for that matter deciding, which they might have to do if government aid were to go to teachers of "the Christian religion" only.
Second, Meade himself was well aware of Madison's Remonstrance and did not believe that passage showed him to be a Christian. Indeed, Meade notes the Remonstrance was largely directed to orthodox Christians and, in order to be effective, had to "draw up on the supposition of the truth of Christianity." Most of the document, however, uses generic philosophical language which was the "bridge," the Lingua Franca if you will, between the orthodox and the heterodox.
In any event, here is the entire passage from Meade's Old Churches in context:
In the neighbourhood of Orange Court-House, at Montpelier, lived Mr. James Madison, once President of the United States, and relative of Bishop Madison. Having been often asked concerning his religious sentiments, I give the following, received from the Rev. Dr. Balmaine, who married his near relative, and by whom Mr. Madison himself was married. Mr. Madison was sent to Princeton College,—perhaps through fear of the skeptical principles then so prevalent at William and Mary. During his stay at Princeton a great revival took place, and it was believed that he partook of its spirit. On his return home he conducted family worship in his father's house. He soon after offered for the Legislature, and it was objected to him. by his opponents, that he was better suited to the pulpit than to the legislative hall. His religious feeling, however, seems to have been short-lived. His political associations with those of infidel principles, of whom there were many in his day, if they did not actually change his creed, yet subjected him to the general suspicion of it. This was confirmed in the minds of some by the active part he took in opposition to every thing like the support of churches by the Legislature, in opposition to Patrick Henry, Governor Page, Richard Henry Lee, and others. This, however, ought not to have been sufficient to fix the charge upon him, as George Mason and others, whose faith was not questioned, agreed with him in this policy. A reference to a memorial against any such act by Mr. Madison, at the request, it is affirmed, of some non-Episcopalians, will show his character and views. It is by far the ablest document which appears on that side of the question, and establishes his character for good temper as well as decision. It is drawn up on the supposition of the truth of Christianity. It must indeed have done this in order to be acceptable to those by whom it was solicited. Whatever may have been the private sentiments of Mr. Madison on the subject of religion, he was never known to declare any Hostility to it. He always treated it with respect, attended public worship in his neighbourhood, invited ministers of religion to his house, had family prayers on such occasions, — though he did not kneel himself at prayers. Episcopal ministers often went there to see his aged and pious mother and administer the Holy Communion to her. I was never at Mr. Madison's but once, and then our conversation took such a turn—though not designed on my part—as to call forth some expressions and arguments which left the impression on my mind that his creed was not strictly regulated by the Bible. At his death, some years after this, his minister—the Rev. Mr. Jones—and some of his neighbours openly expressed their conviction, that, from his conversation and bearing during the latter years of his life, he must be considered as receiving the Christian system to be divine. As to the purity of his moral character, the amiableness of his disposition toward all, his tender affection to his mother and wife, kindness to his neighbours, and good treatment of his servants, there was never any question. [My emphasis.]