I think Sun would be Christian. Like I imagine that getting out of the daycare and experiencing the outside world for the first time without Moon to hold his hand, he probably stumbled across some sort of church or flyer advertising one, and heard all about the Lord. He immediately starts developing obsessive compulsive rituals around religion; crossing himself, wearing a cross as a pendant, refusing to curse or say anything related to the devil. He doesn’t really understand that there’s different sects of Christianity, so he sort of just picks up whatever seems like it would work. When Eclipse shows up, he tries to exorcize him, to Eclipse’s utter confusion.
When things calm down, he tries to stop feeding into his compulsions, and actually succeeds for a while. Then, the Bloodmoon hallucinations began, and he fell headfirst back into it, believing that they only showed up because he stopped. His obsession bordered delusions at times, only being able to recover with Moon acting as an authority in all things objective and true. He was being haunted, sure, but his brother was smart and right all the time, and he said that he’d be okay. Even later, he still wears a pendant under his vest, afraid that he’ll attract bad things if he takes it off.
He has a hard time with distinguishing scams in general, due to his lack of knowledge with science. There were several times where he tried to get the family to try out diets and fads, cutting everything from gluten to pasteurized food. Moon and Solar had to work together to explain to him how vaccines worked in order to get him to stop parroting misinformation from the Facebook moms that he gossiped with in the daycare. Moon handles most of the mail for this reason, since Sun is more likely to call spam numbers. Moon has his own delusions and hallucinations to deal with, but it’s mostly surrounding concepts like purity and sacrificial innocence. Sun’s are more focused on things like guilt and rot, both of their delusions stemming from the July 16th incident.