I'm so sorry, OP, but you've just unlocked an unskippable cutscene...
What we can probably say about House religion:
Their overarching theology draws heavily on the Book of Revelation. Specifically, the first and second resurrections of Revelation 20. Housers are "the Children of the Resurrection", the only people (re)made in the image of God, Alecto is "the devil" locked away, whose release will herald the end.
John is God, but they don't seem to practice monotheism as classically understood: i.e. a single god that is omnipotent, omniscient, omnificent, etc. Abigail justifies her heresy by pointing out that John "never claimed omnipotence", Teacher prays that "nothing happen that [John] did not anticipate", and it's not clear whether "the Creator" referenced in the letter read at the muster is to be understood as John or as referencing some greater creation mythos.
They seem to believe in intercessory prayer, but also pray for the Emperor's needs in the same way Catholics pray for the Pope in the Ninth.
They have a concept of sin, and possibly a sacramental system.
There has been some theological development over the course of the empire: Harrow says "it has been thousands of years since anybody bothered to believe in the River Beyond" - House religion seems to have started out with something much more like the Catholic understanding of a tripartite afterlife, with hell, a purgatory that one moves through depending on one's degree of sinfullness, and a heaven. This belief now seems to be something that would get you in trouble with the authorities, and the orthodoxy is rather more like the classical underworld.
They have some kind of religious book, "the Tome". It's unclear whether this is a broader collection of scriptures (perhaps including elements from the Christian Bible) or whether it is solely a collection of religious law - the Eighth are "Keepers of the Tome" and enforce "the justice of the Tome". But it's hard to say whether any of the Bible quotes we get in the series are coming from in world scriptures or religious knowledge, whether they're appearing in the same liminal contexts as Shakespeare quotes do, or a secret third thing.
There is...possibly...some cruciform imagery in House religious iconography, depending on how you read the description of the Mithraeum chapel.
Interesting context to all this is that John was, as far as we can tell from what he tells us, educated in an Anglican school and baptised as a teenager at a non-denominational music festival (in a brief period of belief? A desire to fit in?). Some of his friends in the cow dome were nominally from various Commonwealth Protestantisms. But the only Catholic influence he definitively had was the nun, who seems to have been pushing a very specific metaphysical agenda and who John cautiously and ironically vindicates: "that finding it - the last link between what made someone alive and what made someone dead - would bring us closer to God. She was right, but I'm not sure she was right in the way she meant." The Houses are so very Catholic in part, I suspect, because there was a specifically Catholic context to John's traumatic apotheosis, and because death, resurrection, and memory wipe didn't seem to take the edge off Cristabel's enthusiasm...
But I desperately want more details about what Housers actually believe and what that looks like in peoples' lives.
(I've got further focused and unfocused thoughts on House religion here, if you're interested).