He could try to fight back against this hatred. Naruto has a strong will. Instead of just accepting being hated, he might try to prove everyone wrong. He could start by doing good deeds secretly or try to expose any false rumors that are causing people to hate him.
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.
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 initially be confused. He has always looked up to Sarutobi as a respected elder, so being hated by him would be unexpected. He would probably try to find out why Sarutobi hates him. For example, he might go to Sarutobi and ask directly, hoping for an explanation.
Naruto could also get really sad and start to doubt himself. He might think that he did something terribly wrong, even if he didn't. And he may try to change himself to win back their friendship, like suppressing his usual exuberant personality.
Naruto might initially be very confused. He has always considered Team 7 as his friends, so the sudden hatred would be hard to understand. He could try to talk to them to find out what's wrong, but they might just ignore him or be hostile.
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 If they don't listen, he could become really sad and withdrawn.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.
One reason could be that some fans might be disappointed with certain aspects of the original Naruto series. For example, the development of some characters might not meet their expectations. So, they create fanfiction to express their negative feelings.
He could meet an AU version of Hinata who is more assertive and outgoing. Maybe she's a powerful ninja in her own right and not as shy as in the original story.
Naruto could try to communicate. He could sit down with his family members and try to understand why they hate him and also explain his side of the story.