Well, Naruto's disregard for the prophecy might make some characters respect him more. For example, Sasuke could see Naruto as more of an individualist, breaking free from what's 'predetermined'. It could also make his friends like Shikamaru and Kiba see him as a bit of a rebel in a good way. They might be more intrigued by his independent thinking.
Since Naruto doesn't care about the prophecy, he might get into conflicts with the village elders or those who believe in the prophecy. This could lead to him being ostracized for a while, but then he could prove that his way is also valid by achieving great things on his own terms. Maybe he discovers a new power source that has nothing to do with the prophecy - bound powers.
In this fanfiction, Naruto's hatred for weaklings might strain his relationships. He may come across as harsh to those he deems weak, causing them to be afraid or resentful. For example, his friends who might be going through a tough time and seem weak temporarily could be pushed away by his attitude.
Well, it could make his relationships quite complicated. For example, with Sakura, his lack of understanding of love might lead to him misinterpreting her signals. He might see her as just a good friend when she has deeper feelings for him. And with his friends like Sasuke, Naruto's confusion about love could make it hard for him to fully support Sasuke in matters that are related to love or emotional bonds, as he doesn't really get it himself.
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.
Well, in such a fanfiction, it could make Naruto more self - reliant. Since his mother doesn't care, he might have to find strength within himself. He could become more determined to prove his worth not just to others, but also to himself.
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 lack of trust could lead to a lot of misunderstandings. For instance, if someone tries to help him but he misinterprets it as a malicious act because of his distrust. This can create a cycle of more distrust as others start to feel frustrated with him.
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 relationship with Sasuke would be greatly affected. Sasuke, who has always been somewhat defined by his rivalry with Naruto as a shinobi, might not know how to interact with Naruto anymore. They could grow apart as Sasuke still pursues the shinobi path while Naruto abandons it.
His overprotectiveness towards his sibling might make his friends a bit cautious. They might not want to involve Naruto's sibling in any dangerous missions or activities for fear of angering Naruto. For example, Kakashi might be more hesitant to let Naruto's sibling go on a mission with the team.