Perhaps Percy hates it because it creates a lot of plot holes and inconsistencies in the world he knows. If there's a son of Artemis in fanfiction, it might mess up the way the gods' relationships and powers work in the original story.
One possible reason could be differences in their divine natures. Percy is a son of Poseidon, a god associated with the sea and a more fluid, emotional element. Artemis is a virgin goddess of the hunt, very strict and unyielding in her ways. This contrast in their essences might lead to clashes and Percy's dislike.
It might be due to the way their goals are presented in fanfiction. Naruto is often about protecting his village and friends. If Artemis's goals in the fanfic are in conflict with Naruto's, like if she's more focused on her own self - interest in the story, Naruto would hate her.
One possible reason could be that Naruto, coming from his own world with its own power system, might view the gods in Percy Jackson's world as too powerful and controlling. He's used to relying on his own ninja skills and the power of friendship, and the idea of these all - powerful gods might seem unfair to him.
One reason could be that Percy is loyal to Annabeth. In the original series, his relationship with Annabeth is strong, and he might not want to betray that for Artemis. Artemis is also a virgin goddess, which adds a layer of complexity to any potential relationship.
One possible reason could be a misunderstanding. Maybe Artemis misinterprets Percy's actions as being against her or her hunters. For example, if Percy accidentally endangers one of her hunters during a quest, Artemis might see it as a betrayal of her trust in him.
Perhaps Tails feels that fanfiction undermines the hard work of the original creators. He might think that the official story should be the only source of information about him and his adventures, and fanfiction is an unwanted deviation from that.
One possible plot could be that the son of Artemis discovers a threat to the demigod world that is related to his mother's domain. He then seeks out Percy for help because of Percy's reputation. Together, they embark on a journey to find a magical artifact that can stop the threat.
One possible reason could be jealousy. Maybe Percy gets more attention or recognition in their fictional world that makes Annabeth envious and thus appear to hate him.
Jiraiya was a serious shinobi with a certain code. Fanfiction might play around with that code too much for his liking. It could make light of things he held in high regard, like his loyalty to the Leaf Village or his training of Naruto. So that's a possible reason for his hatred.
Perhaps it's due to the interference of the gods. The other deities might not approve of their relationship for various reasons. Maybe Zeus, fearing the power that could come from a union between Percy and Artemis, decides to put an end to it. In the world of Percy Jackson, the gods often meddle in the affairs of mortals and demigods, so this could be a factor.