That is a very interesting site. Thanks for posting it.
All three of these critiques appeared in the Millennial Harbinger, but, as the following says from the link below, the first set of articles critiquing the Book of Mormon was from 1831, many years before the link I first provided.
“This review of Mr. Campbell came out first in the ‘Millennial Harbinger’, a monthly periodical published by him in Bethany, Virginia, under date of February 7th, 1831.”
http://www.mun.ca/rels/restmov/texts/acampbell/delusions.html
Alexander Campbell was one of the founders of the Restoration Movement, which basically said that all the truth we need to know is in the Word of God, meaning the Bible. Additionally, the movement described the need for unity in core principles, but allowance in non-core principles. Of course, determining the line between such areas could be difficult.
This movement had no actual leader, though. Campbell, nor others, were ever “in charge.” It was a fully decentralized approach to Christianity.
That said, one movement that came out of that was the Disciples of Christ Christian church, which did start a centralized governing body. The other two lines of churches the movement spawned was the much larger collection of independent Church of Christs throughout the country, and the smaller collection of Christian churches, which somewhat mirror the Church of Christ, but have basically allowed musical instruments.
Of these, in order of liberalism in the current day, the Disciples of Christ is by far the most liberal (15 years ago it was endorsing gay rights parades), followed by the Christian church (many are now contemporary services and many don't have problems with divorced elders, etc.), followed by the Church of Christ (of which there are probably 20+ strains of mostly conservative bodies). The United Church of Christ has a small connection with the Disciples of Christ, but really came from the merger of the Congregational, Evangelical, and Reformed churches primarily.
I would never willingly attend a UCC or a Disciples of Christ church, as both are extreme to very liberal now.