In leafing through the book, I noted a great quotation of Franklin's on Priestley, one I had seen before but forgotten. It was to Benjamin Vaughan, October 24, 1788, the relevant part of which reads:
Remember me affectionately to good Dr. Price and to the honest heretic Dr. Priestly. I do not call him honest by way of distinction; for I think all the heretics I have known have been virtuous men. They have the virtue of fortitude or they would not venture to own their heresy; and they cannot afford to be deficient in any of the other virtues, as that would give advantage to their many enemies; and they have not like orthodox sinners, such a number of friends to excuse or justify them. Do not, however mistake me. It is not to my good friend's heresy that I impute his honesty. On the contrary, 'tis his honesty that has brought upon him the character of heretic. ...
Franklin admired men honest enough in theology to come to terms with their heresy.
Surprisingly, Priestley (probably mistakenly) concluded Franklin was a strict Deist or atheist (quotation forthcoming). Yet, in his letter to Ezra Stiles shortly before his death, Franklin expressed belief in a kind of "Christianity" that almost perfectly mirrored Priestley's:
Here is my Creed: I believe in one God, Creator of the Universe. That He governs it by his Providence. That he ought to be worshipped. That the most acceptable Service we can render to him, is doing Good to his other Children. That the Soul of Man is immortal, and will be treated with Justice in another Life respecting its Conduct in this. These I take to be the fundamental Principles of all sound Religion, and I regard them as you do, in whatever Sect I meet with them. As to Jesus of Nazareth, my Opinion of whom you particularly desire, I think the System of Morals and his Religion as he left them to us, the best the World ever saw, or is likely to see; but I apprehend it has received various corrupting Changes, and I have with most of the present Dissenters in England, some Doubts as to his Divinity: ...
"Corrupting changes" of course, refers to a term Priestley coined -- "the corruptions of Christianity." And it had specific meaning: 1) original sin, 2) trinity, 3) incarnation, 4) atonement, and 5) infallibility of the Bible. "The present Dissenters in England," of whom Franklin, following Priestley, considered himself like minded, "[d]oubt[ed] Jesus' [d]ivinity," and accordingly, rejected those "corruptions of Christianity," those five points, which to the orthodox formed the heart of "Christianity."
In the end, I think Priestley would be satisfied with the kind of "Christianity" Franklin, at his death, embraced.