Unitarian Universalism is perfectly compatible with the pandeist theorem, although since it lacks any specific ``authoritative'' creed or dogma each Universalist chooses their own personal view, or lack of view, of Deity. Over half of Universalists indicate that they are agnostic or atheistic and thereby lack any particular vision of a necessary God at all. The purpose of the religion is not so much to worship a dualistic Creator God (although some do) as to participate in shared spiritual and ethical growth in a community social setting, where my use of the term ``spiritual'' in this sentence is not necessarily any sort of supernaturalism (although it may be, according to the personal inclinations of each individual), but rather describes that part of the inner contemplative aspect of human nature that is the wellspring of religious impulses in the first place.
The roots of Unitarian Universalism appear to date back to the earliest forms of Unitarian apostolic Christianity, but were declared heresy at the infamous Council of Nicaea in 325 CE when Trinitarianism was established as the orthodox creed and that creed was subsequently enforced with torture and mortal sanction throughout the Holy Roman Empire. It was rediscovered (or reinvented) during the turmoil of the reformation in the sixteenth century by a Spanish physician, Michael Servetus, who was (naturally) burned at the stake for his trouble. His heretical works, however, survived and by the end of the sixteenth century Unitarian churches began appearing in communities that would tolerate them. Their creed began by rejecting the divine truth of the Bible, but continuing to view it, and the life and teachings of Jesus, as a source of moral inspiration. In particular, it rejected:
Universalists have emphasized using reason and common sense to assess the claims of all religious and spiritual writings from all the world faiths, rejecting as mythology things that seem implausible while still accepting as insight or wisdom those parts that seem ethically or spiritually praiseworthy (continuing to use spiritually without supernatural connotation). Initially it was based primarily on de-mythicized Christian scriptures, but relying as it does on the judgement of each individual it has long since embraced the ``good parts'' of Buddhism, Christianity, Paganism, various Spiritualisms, Sufism, Bahá'i and more, viewing all of these as myths that nevertheless can help us gain insight into our spiritual selves and seek personal salvation.
Salvation, of course, is not necessarily defined or viewed in the same way that it is in Christianity or Islam; it is more akin to the Enlightenment of Buddhism or Hinduism (and a significant number of Universalists view themselves as primarily Buddhist in their core personal beliefs). To the extent that it is Christian, it is akin to the beliefs of Christian Universalists (who differ only in that they retain some formal Christian theistic structure, rejecting eternal damnation while nevertheless retaining Jesus as God made manifest, the model of a perfect human, and the ultimate source of salvation by means of a reconciliation of each human soul with God).
Because Unitarian Universalism is obviously rather a non-theistic potpourri, it equally obviously can be in complete agreement with the theorem above, to the precise extent that each and every individual Universalist learns of the theorem, assesses its validity for themselves, decides for themselves if they do choose to believe in God (the condition of the theorem) and then conclude that God is indeed Universal. It is certainly consistent with what appears to be the core beliefs of Unitarian Universalism in general, right down to the fact that it leaves the personal choice of whether or not to believe in the probable existence of God up to each individual based on their own experience and assessment of the remarkable data of their own sentient existence.
Outside of that, I personally think that Universalism is a perfectly lovely religion, a rational religion. It focuses on ethical humanism and the practical need to foster a rational ethical society that does not rely on Bronze Age supernaturalist or theistic mandates as its basis. It leaves the choice to believe or not believe in God up to each individual without making any dogmatic statement about it either way, permitting atheist and deist alike to participate in non-supernatural spiritual growth and religious fellowship. It provides a social platform for marrying and burying, the moral instruction of youth absent any extortionist brainwashing, for doing good works together. Not everybody ``needs'' to participate in such an organization, but many do, and even if reason tells one that there is no God and death is just death, death of a loved one is a tragedy and it is easier to bear when the burden is shared by a supporting fellowship and community.
I therefore have to give it strong marks, and openly invite Universalists to contemplate the theorem proven in this work as a possible rational basis for the further progression of Universalist conditional belief.