You can read Priestley's collection of letters to the Swedenborgs here. I'm not the first person to find these. A book in 2007 nicely sums up their contents.
Here is what Priestley writes on page two of the book:
We view with equal horror the doctrine of the trinity, consisting of three persons in one God, as equally absurd and blasphemous; constituting, in fact, three gods. For such you agree with me in thinking that three persons, each possessed of every attribute of divinity, must necessarily be, and that this doctrine is as contrary to the uniform sense of scripture, as it is repugnant to reason and the plainest common sense, though sanctioned by the most solemn decrees of councils from that of Nice to that of Trent, and by the united force of all the civil powers, in most unnatural alliance with the church of Christ.
We also agree in reprobating the whole system which has now obtained the name of calvinism, though it originated with Austin, and has been introduced into all the established creeds; a system which represents the whole human race as so fatally injured by the sin of Adam, that they retain no natural power of doing the will of God; so that had none of them been exempted from the sentence of condemnation by an arbitrary decree, they must all have been doomed to the pains of hell for ever;...
The Swedenborgians were neither unitarians nor trinitarians but believed (if I understand them right) the Trinity existed in ONE person -- Jesus Christ (that is they believed in some form of the modalist heresy). They believed in other odd doctrines that merited them the label "heretic" (just as with Priestley).