I'm going to post later on what Philip Clayton and Steven Knapp call a minimalist personal theism as the basis for being church, but I thought I'd post first from Hoadly, whose works I studied during my Ph.D. studies (though my focus was on Hoadly's maximalist opponents).
It is useful to start with Hoadly's understanding of authority. It's helpful to note that he was seeking a way of accommodating into the national church those persons who were of Presbyterian and Congregationalist sympathies. While he affirmed the role of the government in ordering the religious arena, he believed that ultimately it was the conscience of the individual not the rulings of the church that should prevail.
So, he writes that Christ is the sole law giver and judge with regard to matters of conscience and salvation. In a pamphlet entitled the Nature of the Kingdom, or Church of Christ (1717).
And in the sense therefore, "His kingdom is not of this World;" that he hath, in those points, left behind him, no visible, human authority; no Vicegerents, who can be said properly to supply his place; no interpreters, upon whom his subjects are absolutely to depend; no judges over the consciences or Religion of his people. For if this were so, that any such absolute Vicegerent authority, either of making new laws, or interpreting old ones, or judging his subjects, in religious matters, are lodged in any men upon earth; the consequence would be, that what still retains the name of the church of Christ, would not be the Kingdom of Christ, but the Kingdom of those men, visited with such authority. (The Works of Benjamin Hoadly, 1773, 2:404).
Further Hoadly defines the church and its membership in this way:
And the notion of the Church of Christ, which at first was only the number, small or great, of those who believed him to be the Messiah; or of those who subjected themselves to Him, as their King, in the affair of Religion; having since that time been so diversified by the various alterations it hath undergone, that it is almost impossible so much as to number up the many inconsistent images that have come by daily additions, to be united together in it: nothing I think, can be more useful, than to consider the same thing under some other image, which hath not been so much used; nor consequently so much defaced. (Works, 2:404).
For Hoadly there is no perfectly defined version of the Church of Christ. We have what we have, and the key is to be faithful and to practice our faith with sincerity. Thus, concerning the peace and unity of the church and Christ's realm, he writes:
The peace of Christ's Kingdom is a manly and reasonable peace; built upon charity, and Love, and mutual forbearance, and receiving one another, as God receives us. As for any other peace; founded upon a submission of our honesty, as well as our understandings, it is falsely so called. (Works, 2:409).
As you might expect, Hoadly was rather controversial, and not well appreciated in his time, though he was a favorite of some in the royal family, so he did rise to prominence. Still, he wrote in a way that offered later Christians an opportunity to broaden their horizons. There is much affinity, for instance, between Hoadly's Latitudinarianism and that of Alexander and Thomas Campbell (they also had an affinity for Locke).
The question is -- can this minimalist view of doctrine be sufficient for the existence and health of the church?
For more on Hoadly see William Gibson's Enlightenment Prelate: Benjamin Hoadly, 1676-1761,
(James Clarke, 2004).