One possible reason could be envy. If Naruto suddenly gains a great deal of power or attention in the fanfiction, his friends might feel left out or jealous. Another reason could be a misunderstanding. Maybe Naruto is framed for something he didn't do, and his friends believe the false accusations without giving him a chance to explain. Also, in some fanfiction, a change in Naruto's personality, like becoming overly aggressive or secretive, could lead to his friends growing to dislike him.
He could start by having an honest conversation with his friends. Explain his side of the story clearly. For example, if it was a misunderstanding, he can show evidence to clear his name.
At first, Naruto might be really confused. He's used to thinking of his friends as his support system, so when they turn on him, he doesn't understand why. He'll probably try to talk to them, to ask what he did wrong. If they don't listen, he could become really sad and withdrawn. Maybe he'll start training even harder, using the pain of being rejected by his friends as motivation to become stronger.
In some fanfictions, Naruto might be hated by his friends due to a misunderstanding. For example, if there's a false rumor spread about him being a traitor. Another reason could be his sudden increase in power that makes his friends jealous. Maybe he accidentally harms one of them during a training session and they hold a grudge.
He might try to prove himself. Naruto has always been a determined character. So he would likely strive to show his family that they are wrong about him. He could do this by achieving great things in the ninja world, like mastering new jutsus or completing difficult missions.
In fanfiction where Naruto is hated by his family, it could be a very dark and angsty take. Maybe the author wants to explore the idea of Naruto facing even more hardships on top of being an outcast in the village. It could lead to a very different Naruto, one who is perhaps more bitter or desperate for acceptance outside of his family unit.
Maybe in that fanfiction, Naruto's over - eagerness to be recognized could be misconstrued. His loud and boisterous nature might annoy people. For example, if he constantly interrupted others or pushed his ideas too hard without considering others' feelings, it could lead to dislike.
Naruto might also be determined to change his brother's mind. He would keep showing his good side, like his kindness and his strong will to protect the village. He could think that by being a better person, his brother will eventually stop hating him. He may even go through some tough training to prove himself not only to his brother but also to the whole village. And in the process, he may face a lot of difficulties and rejections from his brother, but he won't give up easily.
Naruto could develop a very different personality. Instead of his usual cheerful and determined self, he could become withdrawn and angry. This new personality would affect his relationships with others in the village, and might even make some people fear him more than they already did.
It's not overly common, but it does exist. A lot of Naruto fanfiction tends to focus on other aspects like his relationships with his friends or his growth as a ninja. However, the concept of his parents hating him can offer a unique and often darker take on the character. Writers may use this to show a more jaded Naruto, one who has to overcome not just the hatred of the village but also from his own family.