The plot may start to revolve around the family's struggle without Naruto's help. This could involve them trying to prove that they can manage without him or trying to find a way to make Naruto change his mind. At the same time, Naruto's own journey might continue separately, but his actions or lack thereof will always be in the background of the family's situation. It could also lead to new alliances or enemies being formed as a result of the family's new situation without Naruto's support.
Maybe he has some personal grudges or misunderstandings within the family in the fanfiction. It could be that something happened in the past that made him feel betrayed or unappreciated, so he refuses to offer help.
It would likely create a lot of tension. Family members might be confused and hurt by his coldness. They may try to reach out to him but be constantly rebuffed, which could lead to feelings of sadness and helplessness among them.
Perhaps Naruto has found a new purpose or community outside of Konoha that values him more. He may be so content with his new life that he simply doesn't want to get involved with Konoha's problems anymore. Konoha's actions towards him could have made him realize that his loyalty was misplaced all along.
It may also lead to Naruto making different choices. Instead of relying on his family for support, he might turn to other sources. This could drive him closer to some characters he wouldn't have been close to otherwise, and change the power dynamics in the story. For instance, he could side with a group that his family is against, just to show his independence from them.
Naruto's character development has always been about self - discovery and growth. He starts as an outcast and rises through his own determination. By the time of the fanfiction, he might refuse peerage because he doesn't need external validation in the form of a title. His growth has made him confident in who he is without such trappings.
The village would likely be in a state of panic. Since Naruto is very powerful, without his help, they might be vulnerable to attacks. They would have to find other ways to defend themselves, which could be difficult.
His friends might respect his decision more. They know how powerful the Kyuubi's chakra is, but also understand Naruto's reasons for not wanting to use it. This could strengthen their bond as they see Naruto's integrity.
Well, it might make Naruto more isolated in the fanfiction world. His non - acceptance could push him away from potential allies who are related to his family. This isolation can then lead to new adventures as he tries to find his own path without his family, thus shaping the plot in a different direction. For example, he might go on a journey to discover the truth about his family on his own, and along the way, he meets new characters and faces new challenges that form the plot.
His non - acceptance might also attract the attention of enemies. If his family has some power or influence, the enemies might see Naruto's rejection as a weakness or an opportunity to create more chaos. So, it could drive the plot towards a more action - packed and dangerous direction as Naruto has to deal with external threats while also dealing with his family issues.
The plot could take a very emotional turn. His family might be heartbroken and try to find him, which can drive a big part of the story. Meanwhile, Naruto himself could be going through a lot of self - discovery. He might become stronger or change in ways that are both positive and negative as a result of leaving his family. This can then have a huge impact on how he interacts with the world and the people he meets later in the fanfic.