Now we come to the nearly ``generic'' non-theisms - the various flavors of deism. Deism is simply a belief in God, often identifying God as the creator of the Universe but not necessarily as a dualist sort of creator. Deism is not a creed with a specific scriptural theism, and deists are generally rationalists who elect to believe in God but otherwise completely accept the scientific process as leading to truth. Consequently (lacking any evidence to the contrary, and motivated by a correct definition of ``natural'' that identifies Nature and the Universe) deists generally believe in a perfectly natural Universe devoid of any sort of supernaturalist miracles.
Individual deists (and schools of deism) differ greatly in what they believe in concerning e.g. the human soul, afterlife, creation, the existence of a moral imperative from Deity, postmortem divine justice. They are more or less united in rejecting all forms of theism and at the very least viewing any reports of miracles or supernaturalism with the greatest possible degree of skepticism.
Historically, many of the Founding Fathers of the United States were deists: Jefferson, Franklin, Paine were prominent deists and both spoke and wrote extensively against theism. Lincoln was either an atheist or a deist - he was forced to pretend to being a Christian because Christians are ruthless to politicians who do not share their personal theistic delusion (where I call it a delusion in the precise sense that it violates the proven theorem above and hence is self-contradictory and cannot be correct as it is theistically specified in the Bible).
Deism is conditionally compatible with the pandeist theorem. A deist who believes in a distinct, dualistic God who created the Universe is obviously inconsistent. Such a thing is impossible, because God (if It exists) is at the very least part of the Universe, the set of everything that exists. God could therefore never create the Universe quite aside from whether or not God is the Universe - that's a simple contradiction of what the words mean. A deist who believes in God that is the Universe is a pandeist, and is not only compatible with the theorem, but is now affirmed in their conditional belief as being demonstrably proven as a theorem of information theory.
This leaves open many questions about a conditional pandeist or deist belief system - whether or not God is sentient, whether or not God (granted sentience) cares about morality, whether or not a system of perfect justice is plausible, whether or not a Universal awareness or soul exists that can mediate any sort of perpetuation of life experience. All of these should be legitimate areas of metaphysical, reason-based speculation, with the firm understanding that the resulting systems of belief, no matter how consistent and hence not actively impossible are likely to all remain moderately implausible in the absence of reliable affirming evidence.