About a day after I posted
this, my mom who was also raised unitarian called me. She explained, it's all in how you think about it. John Adams attended a number of churches in his life, but generally tended to belong to Congregationalist congregations (that's fun to say). The Congregationalists are basically the product of a bunch of groups that had splintered off from the Anglicans merging together. Restricted in England, they fled to Massachusetts and other New England colonies, where they formed a new socio-religious environment, in which John Adams would be born and raised.
The Congregationalists are, as I said before, an ironically named congregation - a group of churches bound into an organization that has a highly specific set of beliefs. In the case of the Congregationalists - they historically believed in a grassroots "Christianity" where authority derived more clearly from social processes that any one could perform rather than initiation into a select and powerful clergy.
On the other hand unitarians aren't a congregation, not any more than trinitarians are (which would include Catholic, Orthodox, and various Protestants among other congregations). But, as the definition of Congregationalists suggests, they can easily be members of many (but not all) congregations, and historically have been (in Anglophone communities) strongly associated with Congregationalists.
Do you see the trick there? You could historically be a Congregationalist and a unitarian. Or a Congregationalist and a trinitarian. Or a unitarian and something other than a Congregationalist. I'm assuming you can understand this.
Warren Throckmorton gets this, and excellent explains the debates leading up to the schism in 1825.
That's the point at which the debate between the unitarian or similarly "liberal" congregationalists and trinitarian or similarly "conservative" congregationalists splintered. Unitarianism had literally become the unofficial ideology of the congregational church, but there was no acknowledgement of this, with a small powerful social clique in charge of the church which insisted on an explicitly trinitarian line in the church. Something had to give way, however, between populist opinion and professional authority.
In 1825, the religious community splintered, with the majority of the churches leaving, founding a new, explicitly unitarian community. At that point, a congregation, for the first time in the anglophone world, came into being which explicitly denied the existence of the Holy Ghost -
this congregationalist source briefly mentions it (in the "Heritages" section).
This, as my mother put it, was how he somehow led himself to believing that unitarians were trinitarians until some point in the early nineteenth century. I feel like I have to point out that that's patent nonsense - the unitarians who attended Congregationalist churches overwhelmingly didn't accept a variant of unitarianism that would have accepted the existence of an entity reasonably called the Holy Ghost or Holy Spirit. They believed in a singular deity, who unlike the trinity has no ghosty bit. Considering how unwelcome unitarians were at most other congregations until that point and how secretive unitarians had become (because of that unwelcome attitude), unitarians rarely publicly declared their disbelief in the trinity. And believing that because they didn't commit such statements to publicly posted papers renders them historically invisible.
My religious tradition, which both the second and third presidents of this country believed in, becomes identical to the majority's. We are assimilated in the mind of David Barton and those like him - we disappear, as just another trinitarian sect (well, at least until some mysterious point in the early nineteenth century). And the history of Christianity in the United States becomes just that much blander, without us.
As for how the 1825 schism became the 1839 religious reform, I'm not clear. In increasing order of I-was-right-and-David-Barton-is-asinine:
1. He just threw out a date to make it sound like he knew what he was saying (I was wrong, he's focusing on a misunderstanding of the schism alone and he's just a garden variety douche, who's quite sure of himself).
2. He threw out that particular date after confusing it with the publication of The Latest Form of Infidelity (I was kinda right, he's somewhat confusing the schism with
how the conception of God changed and he's quite sure that he understands those peoples' history when he doesn't, aka he's a kyriarchic douche).
3. He threw out that particular date intentionally, thinking that the schism and the debate over the nature of God were related (I was completely right, he's thinking about the date and understanding the schism through that skewed lens and he's a complete ass for thinking he's qualified to speak about those people, ie my religious tradition).
I think my money's on door number two.