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.
Some characters who also have grievances against Olympus might be drawn to Percy. They could form a sort of anti - Olympus group. However, there could also be characters who think Percy is going too far. His hatred could divide the community of characters, with some seeing him as a rebel and others seeing him as a troublemaker.
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 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.
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.
Well, it could really damage his friendships. His friends might be shocked or scared by his outburst and start to distance themselves from him. They may not understand why he lost his temper and think he's become a different person. For example, if he yells at them during his fit of anger, they could take it personally and feel hurt.
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.
Well, it might make him more withdrawn from his friends. If he hates his family, he might be less trusting of others in general. So, his friendships could become strained as he struggles to open up to them.
His skill with the bow might make him more respected. Other characters would see him as a valuable asset in battles or hunts. They might rely on him more, which could strengthen their bonds.
It could also affect his friendships. Some friends might try to convince him to let go of his hatred, which could cause friction. On the other hand, some friends might support his stance, which could lead to them being at odds with the clan. For example, Sasuke, who has his own issues with his clan, might react in different ways depending on Naruto's situation.
With the younger demigods, he would be more of a father figure. He would offer guidance and protection. For instance, he could teach them how to control their powers better, just as Chiron taught him when he was younger. His approach would be more mature and strategic.
The black chakra could make other characters view Naruto with suspicion. His friends might be worried that this new power is corrupting him, which could strain their relationships. For instance, Sasuke might see it as a sign that Naruto is becoming more like the enemies they've fought.