On the other hand, it could make some characters more sympathetic towards him. They might see his pain and try to help him get over his hatred. This could lead to new and deeper relationships as they try to understand him and his past. However, it could also attract some negative attention from characters who don't like his attitude or who are on his family's side.
Well, it might make him more withdrawn from his friends.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.
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.
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 might also isolate Naruto. If his hatred is too intense and he constantly focuses on it, other members might start to avoid him. They might see him as a liability or just someone who is too consumed by negative emotions to be a reliable teammate in the Justice League.
On the positive side, it could bring him closer to those who also have issues with his father or the old ways. There might be some characters who have been wronged by Naruto's father's decisions in the past. Naruto's hatred could make them form an alliance of sorts, united by their shared negative feelings. However, overall, it would likely cause more problems than benefits in his relationships.
His hatred might make his relationships with his friends more complicated. For instance, Sasuke might view Naruto's hatred in a different way, either sympathizing with him or trying to convince him to let go of the hatred. This could create some tension or deeper understanding between them.
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.
If Naruto has a physical disability like a broken arm that doesn't heal properly in fanfiction, his friends like Sasuke and Sakura would need to step in and help him more. Sasuke might be more protective, which could change their dynamic from a competitive one to a more collaborative one. Sakura could use her medical skills to try and find a way to heal him, which would bring them closer. His relationship with his teachers, like Kakashi, would also change as they'd have to adjust their training methods.
His relationship with his sensei, like Kakashi, could become more complex. Kakashi would feel guilty for not being able to protect Naruto from the experiments. And Naruto might start to question Kakashi's ability to keep him safe. This could lead to a strain in their relationship at first, but later they could grow closer as Kakashi helps Naruto recover from the trauma of the experiments.
His hatred might make him more distant from his friends. They may not understand his sudden change in attitude towards his family and this could create a rift. For example, Sasuke might be confused as Naruto was always so positive about family before.