A little history written in 1873 by Henry Wilder Foote on how the first Episcopal Church in New England became the first Unitarian Church in America:
Soon after this time, Mr. Freeman began to feel, scruples concerning those parts of the service which expressed or implied a belief in the doctrine of the Trinity. As he said, long after, "There was a certain concealment practiced before about the Trinity. Fisher (of Salem) has a singular way of satisfying his conscience. He was asked how he could read the Athanasian creed when he did not believe it. He replied, 'I read it, as if I did not believe it.' These are poor shifts. Mr. Pyle being directed by his Bishop to read it did so, saying, 'I am directed to read this, which is said to have been the creed of St. Athanasius, but God forbid that it should be yours or mine.' Another man had set it to a hunting tune and sang it. These, I think, would hardly satisfy the conscience of a truth-loving man." Nothing could have been more remote from his own character.
To the growing clearness in Mr. Freeman's opinions on this doctrine, various circumstances probably contributed. First, it was in the very air of the times and the place, as is shown by the way that similar opinions spread in Boston a little later. And then, the favorite authors whose writings he was reading, — particularly Dr. Priestley, of whom he was a life-long admirer, — were strongly anti-trinitarian. His friendly relations also with the Rev. William Hazlitt, an English Unitarian minister, who visited Boston in the autumn of 1784, doubtless had a considerable influence on his mind.
Mr. Freeman, says Dr. Greenwood, "became more and more convinced that the doctrine of the Trinity was unscriptural and untrue, and more and more uneasy in reading passages of solemn devotion in which it was assumed as a Christian truth. It was a season of great mental trial. . . . He communicated his difficulties to those of his friends with whom he was most intimate. He would come into their houses, and say, 'I must leave you. Much as I love you, I must leave you. I cannot conscientiously perform the service of the church any longer as it now stands.' But this little remnant of Episcopalians loved him, as well as he them, and did not wish to let him go. At length it was suggested to him, 'Why not state your difficulties, and the grounds of them, publicly to your whole people, that they may be able to judge of the case, and determine whether it is such as to require a separation between you and them, or not?' The suggestion was adopted. He preached a series of sermons in which he plainly stated his dissatisfaction with the trinitarian portion of the Liturgy, went fully into an examination of the trinitarian doctrine, and gave his reasons for rejecting it. He has himself assured me that when he delivered those sermons, he was under a strong impression that thy would be the last he should ever pronounce from this pulpit. . . . But he was heard patiently, attentively, kindly. The greater part of his hearers responded to his sentiments, and resolved to alter their Liturgy and retain their pastor.
. . . "Thus did Mr. Freeman, by following the dictates of his reason and conscience, become the first preacher in this country of what he held to be a purified Christian faith; and thus, through the means of his mental integrity and powers of exposition, did the First Episcopal Church in New England become the First Unitarian Church in the New World.["]
This went down circa 1786.
I reproduced this passage in part because I want to stress the dynamic that it should be utterly understandable that Founding era men who disbelieved in the Trinity could worship in Trinitarian Churches, having nowhere else to go or otherwise being wedded to the churches in an "institutional" sense. Indeed there were unitarian ministers in Trinitarian churches, some of whom "reformed" them into Unitarian churches.
Hopefully that above passage will shed light on what it felt like to be a dissenter in a Trinitarian Church who had to put up with hearing and in some cases begrudgingly reciting orthodox doctrines in which one didn't believe.