@Yolech If you want a doctrinal equivalent to Original Sin in Tearmoon, the closest thing would be the villain of the entire series: The Chaos Serpent. From Valentina's description of it, and something that Mia and Citrina agree with, is that the Serpent is an inherent part of human nature, arising from humanity creating winners and losers. The nature of the Serpent being knowledge is also akin to how the original sin is partaking of the fruit of the Tree of Knowledge of Good and Evil. And there's also the plainly obvious parallel of Chaos Serpent = the Serpent in the Garden. Viewed in that way, the entire series can be said to be a struggle against original sin.
I don't think that it's very productive to look at specific details to compare with IRL religions, mostly because the books deliberately make the details vague and how even within the books, there's already pretty big differences in the specifics of religious practices. The Lulus see God in the trees of the Selance forest while the Equestri see God in their horses. Ludwig's views on religion, based on logical consideration and introspection, are quite different from Rafina's more faith-based beliefs.