In terms of the story's plot, it could lead to Naruto trying to redeem himself in Hinata's eyes. This could involve him going on dangerous quests or changing his ways. It also might make Naruto more isolated as he loses one of the people who used to care about him, which could in turn lead to a change in his relationships with other characters like Sasuke or Sakura.
Maybe in the fanfiction, Naruto has made some decisions that go against Hinata's beliefs or values. Suppose Naruto decides to use a very dangerous and unethical jutsu for power, and Hinata, who is usually very moral, might start to hate him for that.
In a modern fanfic, if Naruto is hated by his family, it could change his entire life trajectory. He may be forced to leave his home earlier than in the original story. This would expose him to more danger at a younger age. His relationships with other characters would also be affected. For instance, his relationship with his teachers might become more complicated as they try to navigate the situation. Additionally, Naruto's view of the world could become more cynical, but he could also strive to create a new family of sorts among his friends, which would be a significant aspect of his character development.
It could create a rift within the overall story's world. Fans who love Naruto might not like this portrayal, which could lead to a divide among the fan base. Also, other characters in the story might have to take sides, either with Naruto or with the team that hates him, causing more conflict and drama within the fanfiction.
The first consequence could be Naruto's emotional turmoil. He would likely feel extremely hurt and confused, as Hinata has always been someone he trusted. This could lead to him doubting his own judgment in relationships. For example, he might become more guarded in future interactions with others.
Naruto might become more withdrawn. He's used to being this energetic and positive person, but after having his heart broken by Hinata, he could lose that spark. He might stop going out as much, avoid his friends, and just keep to himself.
For Hinata, if she's actually innocent, she would be heartbroken that Naruto thought she could cheat. She might have to fight hard to prove her innocence. If she was at fault, she would likely face a lot of guilt and the loss of Naruto's love, which was something she deeply cherished. In the fanfiction world, this could also lead to changes in the social dynamics among their friends. Their friends might be divided, some believing Hinata and some believing Naruto's initial perception. It could create a rift in the whole group.
One possible consequence could be a change in Naruto's power level. If Hinata can control the seal, she might be able to regulate the flow of power from it, which could either enhance or limit Naruto's abilities.
One reason could be his power. His connection to the Nine - Tails makes him extremely powerful. In fanfiction, some in Konoha might fear this power and thus hate him. Another reason could be jealousy. Naruto becomes very popular and respected in the original story. But in fanfiction, some characters might be jealous of his achievements and turn that into hatred.
One possible reason could be a false accusation. Maybe someone spread a rumor that Naruto was involved in a heinous act, and without proper investigation, everyone turned against him.
One consequence could be that Hinata tries to move on but struggles a great deal. She might have a hard time opening up to anyone else in the future. Her self - confidence could also take a big hit. Since she put so much of herself into her feelings for Naruto, having her heart broken could make her question her own worth. Maybe she starts to think that if Naruto didn't love her, then no one will. This could lead to her being more reserved and less likely to take risks in relationships or in other aspects of her life.