Percy Jackson as:

a Christian

a Buddhist

a Satanist

a Catholic

a Scientologist

any other religion that exists in real life or fiction

The basic idea is that prior to going to Yancy Academy, Percy converted to a religion/cult. He does this because he clicked a seemingly interesting link on the Internet, watched a movie with a prominent religion, or joined a clique in a school that worships a god—so on and so on.

When Percy does end up in Camp Half Blood, he tries to convert the demigods to his religion/cult (being a hardcore worshipper of his chosen religion/cult) to either great or little success.

Annabeth, Grover, and Chiron try to convince him that Greek gods do exist, and they're not pagans or rip-offs, to which Percy either responds that they are heathens or simply doubles his efforts to convert them. (He ends up convincing Annabeth to become an atheist by complete accident in the process by power of logic and philosophy.)

Meanwhile, the gods and goddesses in Olympus are watching this drama play out with great dismay or great amusement—depends on the god in question (Zeus is pissed, Poseidon is upset, and Hermes and Apollo are laughing their asses off).

This is all I have for now. Please leave a review or message me if you plan on expanding this idea, and send me a link if you do make a story about it.

Bonus ideas: Percy thinks the gods are

a shadow government pulling the strings behind the scenes (and fundamentally human, which drives Zeus up the wall)

aliens

biological experiments with the codenames of the Greek pantheon (and yet again, fundamentally human, annoying Zeus to no end)

insane asylum escapees who sleep around a lot

mutants

a giant experiment by the government for lols

fans of Greek mythology who have used tons of resources to bring their fantasy world to life

Please try them out.