A good friend of mine sent this to me today, and I believe I have an explanation:
So the Mario RPGs often make reference to events in the platformers, meaning we can safely assume that the Marios in these two game types are the same guy. HOWEVER, this does not hold up when talking about the PAPER Mario games, due to the existence of Mario and Luigi: Paper Jam, which canonized Paper Mario as a separate being, along with Paper Bowser, the Paper Toads, etc. The important thing here is Mario. These two characters, being separate entities with their own lives and histories, can coexist as pure and sinful. Mario is a holy man, but the paper has sinned.
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But that's not all.
Let's talk about HOW exactly Paper Mario dies. Late in the game's story, he, alongside evrcery other playable character, is ambushed and killed by a dark wizard. Dimentio, to be precise. Now, we know for a fact that Dimentio is the most objectively evil of all the villains in Super Paper Mario, so it is not a stretch to assume that he commands some form of hellish power. That being said, I would posit that the only reason why Paper Mario is sent to hell is due to his method of demise. He was killed by a hell wizard! Of course he'll have a hard time going to heaven! Not to even mention the fact that every other character goes to hell, too! Bowser, I get. But Peach? LUIGI??? Never.
The final nail in the coffin here is that, about halfway through the chapter, Mario and the gang actually do manage to get into heaven with little to no problem. How do they do this? Through the power of a Pure Heart. They are cleansed of the evil energy which Dimentio imbued them with, and are thus transported to the Overthere.
TL;DR Paper Mario and Regular Mario are different guys, and neither of them are sinners. Dimentio just hit Paper Mario with this:
