Poc Percy actually makes a lot of sense, and it's sad that because of the series we usually see fanart of that now.
Percy being a poc (black specifically) just makes loads of moments better, imo.
Like it doesn't make sense that the news would see Grover, Annabeth and Percy (all white) and think "Yeah only Percy's a terrorist, the others are innocent" but if Percy was black it'd make total sense. He also refers to these kids he doesn't like as "rich white" kids twice. It doesn't make sense as a distinction if Percy's white.
This one is a little more vauge, but he says that Ares' bike seat looks like it's made of "Caucasian human skin" and not just like regular human skin.
Also, the fact that the dead confederates like Annabeth and Clarrise (sort of) but don't like Percy would make sense. And it's funny to imagine them being like
Confederates : We don't like this one
Confederates: um...Well.. you see- it's
Percy : it's because I'm black isn't it
Confederates: No! Nononononono... it's because...you're from New York right?
Lastly, I think his dynamic with Rachel's dad makes more sense, as well. Obviously, Rachel's dad could just be protective of her, or a snob who doesn't like Percy because he's a "poor troublmaker," but the way they interact was alwasy very like odd.
"'So...I take it your friedn isn't coming to St Thomas?' That's what Mr Dare called me. Never Percy. Just your friend or young man if he was talking to me which he rarely did"
Of course it's just a headcanon, it doesn't need to fit the book, or media, at all. It's just fun tk imagine.