There could also be a shift in the power balance within the ninja world. Other villages might see Konoha as weakened due to Minato's self - sealing and might take advantage of the situation, leading to more conflicts and power struggles among the villages.
One consequence could be that Naruto has a constant struggle to keep Kaguya's power in check. He might experience internal battles within his mind as Kaguya tries to break free.
He might become withdrawn. Instead of being the energetic and outgoing Naruto we know, he could isolate himself from his friends and the village. This would change the whole dynamic of the relationships in the fanfic.
One possible reason could be to protect the village. Minato is known for his self - sacrificing nature. By sealing himself, he might be containing a great evil or power that could otherwise destroy Konoha. For example, if there was a powerful enemy or a dangerous jutsu gone wrong, sealing himself could be a last - ditch effort to keep everyone safe.
One consequence could be that Naruto becomes an outcast in a different way. In the original, he was an outcast because of the Nine - Tails, but here, it could be because of his abandonment. He might not have the same dreams of becoming Hokage. Instead, he could be more focused on survival.
On a more personal level, they could face internal guilt. As Naruto grows up and achieves great things on his own despite their neglect, Minato and Kushina may realize what they've missed out on. This realization could cause them a great deal of internal turmoil and regret for not being there for their son when he needed them.
One consequence could be that Naruto loses some of his humanity. If he is constantly seen as a weapon, he might start to view himself in that way too. This could lead to problems in his relationships with his friends and allies as they might start to fear or be cautious around him.
The consequence could be that the fanfiction community might feel less connected to Minato as a character. Since he is a significant part of the Naruto universe, his dislike of fanfiction could make some fans less enthusiastic about including him in their fan - created stories. This might lead to a shift in the focus of fanfiction towards other characters who are more 'welcoming' of fan interpretations.
The village of Konoha would also be affected. With Minato still alive, he could continue to lead the village and make different decisions. This might change the relationships between Konoha and other villages. For example, there could be more peaceful alliances as Minato is known for his diplomatic skills. Also, Kushina being alive would mean that the Uzumaki clan might have a stronger presence in the village, which could lead to new jutsu developments and a different power balance within Konoha.
One consequence could be that Naruto grows up with an even stronger connection to the Kyuubi's power from a very young age. This might make him a much more powerful ninja earlier on in his life.
Naruto might also face emotional burnout. If he's constantly pushing himself in his relationships, he could end up feeling drained. For example, if he's always trying to be there for everyone but not getting the same support back, he could become depressed or angry. This can then affect his performance as a ninja and his relationships further.