I first came upon this extension of ecumenism into pan-deism among some Roman Catholic scholars interested primarily in the "reunion of the churches," Roman, Orthodox, Anglican]]. [...] We may perhaps ask what is the ultimate aim of the Curia in promoting the pan-deist movement. [...] They do not necessarily discern in Rome's ecumenism and pan-deism a project for world dominion.
Pure Vedantic Hinduism as described in particular in the Upanishads is monist and either pandeist or panendeist - Brahman is the Universe, we (as Atman or "God-souls") are a part of Brahman and Brahman itself, parts separated from the whole to be able to appreciate the whole and ever seeking to rejoin the whole and its perfect state of being as all things. Brahman in the Upanishads is not a being that is worshipped - they make it absolutely clear that Brahman is indifferent to worship and is not the object of worship.
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.
A pandeist scientist or philosopher studying the Universe is not necessarily irrational, nor is he or she particularly distinguishable, from an atheist scientist or philosopher who loves the subject of his or her work.
God is growth, God is structure/knowledge, God is everything and nothing simultaneously. And, rather heretically for the Abrahamic religions, to perceive i.e. to cognate i.e. to be of matter i.e. to be structured energy generating a gravimetric field is an aspect of God relating to another aspect of God through light, which is of course God. In this, the underlying metaphysics are most definitely pandeist.