Priestley’s son recounted:
“It was a source of great satisfaction to him, and what he had little previous reason to expect, that his lectures were attended by very crowded audiences, including most of the members of the Congress of the United States at that time assembled at Philadelphia, and of the executive offices of the government of the United States.”
-- Joseph Priestley, Jr., A Continuation of the Memoirs of Dr. Joseph Priestley (Written by his Son Joseph Priestley), in John T. Boyer, ed., The Memoirs of Joseph Priestley, at 144 (Washington, D.C.: Barcroft Press, 1964).
Priestley was the preeminent expositor of rationalist unitarianism. His unitarianism was not well received by the masses; he was sort of an Abbie Hoffman type of his age -- popular in certain influential circles only, but whose ideas were too controversial for mass appeal. Indeed, in England, a mob burned down Priestley's home over his controversial ideas, after which he fled to America for refuge. That Priestley's religious system presented itself under the auspices of "Christianity," I think, probably made it somewhat easier to sell to the many elite figures who followed him than if it rejected the Christian label and termed itself "Deism" or something of the like.
However, whether his beliefs should be understood as "Christian" at all is debatable. (Again, Mormonism is the proper analogy. Someone who doesn't think Mormonism merits the label "Christian," probably likewise wouldn't think Priestley's "Unitarian Christianity" merits the label either. One could cite Lincoln who once noted calling a dog's tail a 5th leg doesn't make it so.) It rejected, among other things, original sin, the trinity, incarnation, atonement, and plenary inspiration of scripture as "corruptions of Christianity." Only the rational parts of scripture -- those that passed the "reason" smell test -- were legitimately revealed. Surprisingly, Priestley accepted some miracles recorded in the Bible -- the "rational" ones.
Priestley did believe in the Resurrection of Jesus whom he regarded as fully human, albiet perfect and on a divine mission (hence Priestley was Socinian). As such Priestley rejected that Jesus Christ as God made an infinite Atonement for the sins of man, but regarded the Resurrection as the action of a benevolent God doing for the most perfect man what he one day will do for all men.
More importantly, Priestley regarded the Resurrection as rational. And all religious beliefs, including the miraculous, must meet the test of rationality in order to be true.
Priestley's importance is his disproportionate influence on the men who wrote the Declaration of Independence and who framed the Constitution of the United States. Understanding his influence is key to understanding the political theology of America's Founding.