I'm a huge Potterhead and a longtime camper, and the overlap between those two fandoms is a theory-making engine. I think it starts with the obvious structural parallels: two orphan boys who discover a hidden world tied to their identity, get whisked away to a magical training ground (Hogwarts/Camp Half-Blood), and have a prophecy hanging over them. But the real fuel comes from the differences. The 'why has no Muggle ever stumbled into Camp Half-Blood?' question led to a massive theory thread on my Discord about the Mist being a global cousin to Muggle-Repelling Charms, possibly maintained by Hecate, who some link to Morgan le Fay from Potter lore.
Then you've got the magical systems. The debate over whether a demigod's innate abilities would register as 'magic' to a wizard, or if they'd be seen as some kind of non-wand-based power, is endless. I once spent a whole afternoon with friends debating if a child of Hecate could potentially cast Expelliarmus with a wand, or if their magic is just fundamentally different. That blurs the lines and lets fans play 'what if' with characters crossing over. Does Annabeth's brilliance rival Hermione's? Could a child of Hephaestus out-invent the Weasley twins? It's less about who would win in a fight and more about how their worlds' rules would interact, which is the perfect sandbox for theorists.
You also see it with the adults. The Chosen One trauma comparison between Harry and Percy is a deep well for character analysis, but people also love pitting Dumbledore against Chiron. They're both mentor figures with questionable pasts and secrets, guiding their young charges toward a fate they might not fully understand. Theories about them secretly corresponding, or being aware of each other's worlds, pop up all the time. It's that delicious mix of similar archetypes and conflicting cosmologies that keeps the ideas flowing. My personal favorite niche theory is that the Ministry of Magic's Department of Mysteries has a branch studying 'non-wand divine phenomena' and has a file on Percy Jackson marked 'Poseidon's kid, avoid confrontation.'