God, this is such an interesting narrative for the Houses to receive. Because on one level, it's reflective of John trying to create a more loving world than the Christian doctrine that was to some degree forced on him, where people were once absolved of sin they were born into and still need constance vigilance to deserve salvation. But on the other hand, there's an invisible set of people on the other side of the none of them who will never be released from death because they did deserve it, and in his mind there is no forgiveness.
In a way, this is another aspect of how John is an antichrist figure (as in anti-Christ, not "The Antichrist").
In Christianity, death comes into the world through the actions of one man: the sin of Adam. In the Catholic tradition particularly, this is the root of 'original sin', the sin into which every human is born, as OP suggests above. Sin and death is overcome by the actions of God in Jesus' death and resurrection. This is "grace" - God's actions that do not depend on what individual humans might 'deserve', but on the very nature of the divine. (Grace as a concept rather haunts John's story: "a state of grace", "that's the grace of it", etc).
And in the story of TLT, metaphysics-shattering, all-encompassing death also comes through the sin of one man, forever marring those born in its wake. And a seemingly impossible resurrection comes through the choice of a divine figure to intervene in a situation where humanity would have otherwise been hopeless. The awkward thing is that these are the same guy...
Sin in Christianity is an exercise in free will. You can't accidentally commit a sin. You have to mean it. The idea is that God made it possible for humans to choose to do bad things because that's necessary to be able to meaningfully choose to do good things. And without digressing into theological ethics or Dawkins et al or anything like that, the fact that the Houses use this very Christian framing and language is so revealing.
Because John, as "god", is liberating them not from the messy outworkings of their own choices and actions, but from the consequences of his.
And Housers, in this theological landscape, the "children of the Resurrection", do not seem to have much capacity for free will: the scions are called to Canaan House in fulfilment of "the contract of tenderness made on the day of the Resurrection" (GTN ch 3). John may well have hoped to create a more humane system, but House theology seems to be a sort of post-apocalyptic predestination on steroids. The only 'grace' is John's ability to wipe out the memory of his own sins. There is no possibility of transcendence, even for his own chosen few - Abigail Pent's belief that the River can be crossed is a dangerous heresy. Even by his own telling, his 'saints' have committed an "unforgivable sin". It's all rather grim, even before you look outside the system at the people they believe aren't made in the image of god...
