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 its 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 recognize one feature.
So far as I can make out what he's saying is that he (Jefferson) is a true Christian and that the theologians and expounders of orthodox Christian dogma are not. It's a bit confusing what he means by the "vicious ethics and deism of the Jews," but I don't think one can use this quote to maintain that Jefferson was an orthodox Christian. And that's the problem: what some considered to be "true Christianity" might be very different from Christian orthodoxy as understood by the churches.
In some of the delightful conversations with you, in the evenings of 1798-99, and which served as an anodyne to the afflictions of the crisis through which our country was then laboring, the Christian religion was sometimes our topic; and I then promised you, that one day or other, I would give you my views of it. They are the result of a life of inquiry & reflection, and very different from that anti-Christian system imputed to me by those who know nothing of my opinions. To 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 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.
Note the last few words, which indicate that Jefferson's idea of Christ and Christianity was very different from the orthodoxy of the churches.
I don't think anyone can argue that most of the founders were deists. Then as now, self-proclaimed freethinkers were a minority. But the atmosphere of 18th century philosophy and religion were quite different from that of the 16th or 19th century. There was a strong enlightenment component to both religious faith and secular thought in the late 1700s(though defining what enlightenment means in this context could be tricky), and certain key founders had more deism or freethinking in their thought than the average American of the day. Just where Christianity began and ended was much less clear for Washington or Jefferson, Adams or Madison than it would have been for an earlier or later generation. An ethical or cultural Christianity didn't always extend to complete acceptance of orthodox dogma for some of the most prominent of our Founders.
Both sides in this controversy want to claim the Founders or Framers as being wholly in their corner. Learning to recognize that they weren't all wholly orthodox or wholly atheist can be the beginning of wisdom in this question.
I think it wise to remember the position an role the Church of England played in the politics of the time, and to consider how much of Jefferson's (and other's) remarks about religion were directed to the Church.
Most Protestants do consider "true Christianity" to be something different from "orthodoxy as understood by the churches."