Some characters might see Percy as a threat to the hunt. They could try to isolate him or even attack him. This would create a lot of tension in the fanfiction world. On the other hand, there could be characters who support Percy and also start to question the hunt.
It could make other characters who are involved in the hunt feel conflicted. For example, if some of his friends are part of the hunt, they might feel guilty or try to change Percy's view.
With his friends, it could be a mixed bag. Some friends might support him wholeheartedly, which could strengthen their bond. However, others may be cautious. For instance, if a friend has a close relationship with a particular god, Percy's hatred could cause tension. Also, his attitude towards the gods might make it difficult for him to interact with godly allies or enemies. He may be more hostile towards them than necessary, which could change the dynamics of battles or negotiations.
His hatred might make him more distant from the other demigods who still have some respect or hope for Olympus. They may not understand his extreme feelings and this could create tension.
His friends would be devastated. They rely on Percy in many ways, and his sudden absence would leave a big void. For instance, Annabeth might feel lost without him, as they have a deep connection. She would probably be very worried and try to find him.
It could cause a rift among the characters. Some might think he's being selfish by secluding himself, while others might understand his need for privacy. This difference in opinion can create tension and arguments within the group. Also, if Percy has an important role in the group, his absence could make it difficult for the group to function properly in certain situations.
His relationship with clan members might become strained. They may side with their clan heads, causing Naruto to be at odds with them even if he was friends with some of them before. For instance, if a clan member is loyal to their head's views that Naruto opposes.
His friends might be divided. Some who are more inclined to support Olympus might be at odds with Percy. For example, Annabeth, who has a certain respect for the gods, could face a dilemma in choosing between Percy and Olympus.
It might create some division. Some fans who like fanfiction might feel opposed to Jason Grace. While others who respect his view might be more cautious about fanfiction.
It can greatly affect the story. His new role could introduce new settings, like more time in the forest areas where the hunt operates. This would change the scenery from the usual urban or camp settings.
When Percy joins Kronos in the fanfiction, it affects the other characters in many ways. Chiron, the centaur mentor, would be deeply disappointed. He had so much hope for Percy. The minor demigods who looked up to Percy would be lost. They might lose faith in the idea of being a hero. The relationships that Percy had built over the years would be shattered. His joining Kronos would also make the enemy stronger, which would put more pressure on the remaining good characters to come up with a plan to stop them both.
It could also inspire some characters to open up about their own insecurities. If Percy, who seems so tough, can break down, it might give others the courage to share their own fears and doubts.