The Society of Friends, or Quakerism, is another non-theistic offshoot of Christianity that began by rejecting the Bible as divinely inspired truth, and instead viewed Christ Itself as the actual word, or logos, of truth. It further asserted that each and every individual has an inner voice that is of Christ, the Holy Spirit itself, and that proper religious practice is to open one's heart and listen to that voice. It rejects an objectified and dualistic vision of an external, judging deity in favor of the discovery of deity within.
It (with some justice) claims its roots in pre-Nicaea apostalic Christianity, just as do Unitarian Universalists and Christian Universalists. It arose primirily in England in 1650, founded by George Fox, but spread rapidly to the colonies where it flourished. As usual, it was treated as a form of apostasy or heresy by the prevailing Christian churches; as usual, its earliest members were beaten, imprisoned, executed, and deprived of political power and rights before finding a place in the New World where they could more or less be left alone.
Quakers are most definitely non-theists, rejecting creed in the form of theistic revelations that must be clung to against all reason and common sense (where the latter, after all, is an important part of that inner light that illuminates each person's search for truth) while still retaining doctrine - the idea that sure, there have been inspired people in the past who have written things that are well worth reading and that can help lead one to truth, and that some of those writings give a loose structure to the Society of Friends.
I confess that I absolutely adore Quakerism, much as I like Unitarian Universalism, because both focus on personal rational choice, with the Unitarians arguably focussing a bit more on the rational in contrast to the spiritual, the Quakers focussing a bit more on the spiritual in contrast to the rational, but both firmly in touch with common sense and both flexible enough to accomodate new additions to human knowledge and wisdom because they recognize that the human discovery of knowledge and wisdom did not end in the Bronze Age!
Most Quakers I know personally are quite comfortable with physical cosmology, evolution, modern science and simply choose to believe in a Universal Loving God that is a source of personal salvation. To the best of my knowledge, Quaker doctrine does not lean towards universal judgement of sin and eternal hell for those who do not make the cut - to the extent that it is still predominantly if somewhat metaphorically Christian, its core doctrine is close to the creed of Christian Universalists without the assertion of divine truth, but of course each Quaker has to make up their own mind about that, based on their own direct spiritual experience.
Quakerism is (like Universalism) quite broad; there are agnostic and atheist Quakers as well as Christians those with other core beliefs.
Things to really like about Quakerism:
Of course, the real question is, is Quakerism compatible with the pandeist theorem above? Again the knee-jerk reaction must be no - Quakerism originally was a Christian heresy, or return to Apostalic orthodoxy, as you prefer, and hence inherited a lot of Biblical ``baggage'' (that continues to trouble it with inconsistencies as in the case of homosexuality) even as it nominally rejected the Bible as a theistic creed. It is therefore has dualist roots. However, it also has a considerable Universalist character, and I don't know that there is anything in its Doctrine that contradicts the theorem. It is certainly again the case that any Quaker who reads the assertion of the theorem and its proof is free to listen to their own heart and judge for themselves whether or not it is correct, and to indeed treat it as a source of new doctrine and insight into a God that is all things, a God that is awareness in their heart not as a matter of belief but as a direct consequence of a conditional proof in information theory.
So I have to give Quakers very high marks as well as being moderately rational, extremely ethical, remarkably liberal, and capable of encompassing a non-theistic doctrine of a Universal God that does not contradict the theorem above (which is, recall, mute on the question of God's existence and on many of the other hypothesized properties of God beyond omni-this and that that are obvious properties of only the Universe itself).