That is a non-sequitur.
Joseph Priestley did not believe in Jesus' divinity, but believed in his miracles, resurrection and the divinity of Jesus mission. Priestley thought 1. original sin, 2. trinity, 3. incarnation, 4. atonement, and 5. the plenary inspiration of scripture were false "corruptions" of true Christianity ("rational Christianity"). I (mistakenly?) thought Priestley believed in the virgin birth. Maybe he did at one point. I thought I read something from Priestley that argued for the compatibility of both the virgin birth AND Jesus 100% human, 0% divine nature. The logic went something like this: those who argue for a divine Jesus say the virgin birth necessarily means Jesus is divine. No. That is a non-sequitur. Why? Jesus was sent to be a second Adam to correct the first's errors. And the first Adam also was of divine origin but was 100% human, 0% divine.
That is just a paraphrase of what I remember. I will have to read up on where I got it from and the context. And that's because when Joseph Priestley proselytized his Socinian rational Christianity to the Jews, he made it quite clear that he disbelieved in the Virgin Birth along with the Trinity, etc. As he wrote to them [paragraphs added for clarity]:
You expect that your Messiah will be lineally descended from David, and therefore you cannot be reconciled to the idea of Jesus being that Messiah, because Christians say that he had no human father; so that according to your rules of genealogy, he could not be said to be the son of David. But it is no where said that the person who is characterized by the title of Messiah, should be descended from David, but only that prince under whom you are to enjoy.
However, the history of the miraculous conception of Jesus does not appear to me to be sufficiently authenticated. The evidence of it is by no means the same with that of his public life, his miracles, his death and resurrection, which are all that the truth of Christianity requires, (and of which there were many witnesses,) and the original Gospel of Matthew, received by your countrymen, did not contain it.
Your sacred books, as well as ours, being written by men, neither of them can be expected to be, entirely free from mistakes, or exempt from interpolations. Yours, as you must acknowledge, have, in a course of time, suffered in these respects. But it is sufficient for us both, that the great events, on which every thing that is of importance to our religion depends, are true. As to any thing that is not necessarily connected with such events, and therefore is not supported by their evidence, we should think ourselves at liberty to receive or reject it, according to its separate evidence.
Myself, and many other Christians, are no believers in the miraculous conception of Jesus, but are of opinion, that he was the legitimate son of Joseph, who was of the family of David; and such seems to have been the opinion of the great body of Jewish Christians, who had more opportunity of informing themselves concerning the fact than the Gentiles had. But we are not less firm believers in all the public transactions of the life of Jesus, in his miracles, his death, and his resurrection ; and consequently, in his divine mission. With respect to his supposed miraculous conception, and other articles relating to Christianity, but not essential to it, do you examine and judge for yourselves.