If the fight got really intense and out of hand, it could also make Naruto feel pressured to choose sides. However, Naruto being Naruto, he would most likely try to find a way to reconcile them instead. This would show his growth as a person and his ability to rise above family disputes.
It could change the power balance in the ninja world. Other villages might see Konoha as a much greater threat with Minato and Kushina back. On the other hand, it could also lead to more cooperation as they might be seen as a symbol of hope. Emotionally, for Naruto, he would be able to learn more about his family, his heritage, and maybe even get some long - awaited parental guidance which would further develop his character.
On a personal level, for Naruto, it would mean having his parents around. He could finally experience a real family life. Kushina could teach him more about the Uzumaki clan's techniques and traditions. Minato could train Naruto further in his unique jutsu. Emotionally, it would be a great comfort for Naruto and many of his friends who knew about his longing for his parents.
At first, Naruto and Kushina might start to distance themselves from Minato. They could avoid him and not talk to him as much. As time goes on, the hatred might grow deeper. Naruto could start to oppose Minato in public or in important village matters. Kushina might also try to influence others in the village against Minato.
Well, if Minato and Kushina ignored Naruto, it would likely make Naruto grow up feeling extremely unloved and unwanted. He might become more withdrawn and lack the confidence he has in the original story. His drive to be recognized might turn into a desperate need for any kind of attention, not just positive, which could lead him down a much darker path in terms of his character development.
If Kushina and Minato abandoned Naruto in fanfiction, it would completely change the Naruto's character development. Naruto grew up lonely and seeking recognition because he was an orphan. Without their abandonment, he might have had a very different personality, perhaps more confident from the start. Also, the relationships in the village would be different. For example, Iruka might not have had the same special bond with Naruto as he did in the original story.
If Kushina leaves Minato for Naruto in fanfiction, it would completely change the Naruto universe's family dynamics. Naruto might grow up with a different kind of support system. Instead of the absent father figure of Minato, he could have a more present mother figure in Kushina. This could also change his relationship with the village. Since Kushina was an Uzumaki, her presence could lead to Naruto having an earlier understanding of his heritage.
One possible reason could be a misunderstanding. Maybe Naruto gets involved in some dangerous situation and they disagree on how to handle it. For example, if Naruto wants to take on a powerful enemy alone but Minato and Kushina think it's too risky.
Minato might be intrigued. He would be interested in seeing how the fans expand on Naruto's journey. Kushina would be delighted, seeing her son as the center of so many different tales.
Fanfiction can explore their relationship by delving into their unfulfilled time together. For example, showing how Minato and Kushina would have raised Naruto. It could also explore their shared experiences, like how they all have a connection to the Nine - Tails. Maybe in fanfiction, they have family adventures where Naruto learns from his parents' skills and wisdom.
Minato would probably be very proud. He might notice Naruto's use of his own jutsu and be impressed by how Naruto has developed his skills. Kushina would be more emotional, maybe crying at the sight of Naruto growing up so well.