They would likely feel a sense of pride and interest. Seeing different versions of Naruto's adventures and growth in fanfiction would make them proud of how much their son has inspired the fans.
Minato and Kushina's feelings would be complex. On one hand, they would be incredibly proud that Naruto has such a large fan base that creates fanfiction about him. They would be touched by the love and admiration the fans have for Naruto. However, they might also be a bit cautious. Minato, being a former Hokage, might be concerned about some of the fan - created storylines that could potentially mislead the readers about the true nature of the Naruto world or Naruto himself. Kushina, as a mother, would be more interested in the positive portrayals of Naruto, especially those that emphasize his kind heart and strong will. She might get a bit defensive if she reads a fanfiction that doesn't do justice to her son's character.
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.
The story would change a great deal. For one, Naruto wouldn't have the same connection to the Nine - Tails as he does in the original. Minato sealed the Nine - Tails into Naruto, so without that relation, the whole dynamic of the Nine - Tails within Naruto would be different. He might not have the same power - up moments related to the Nine - Tails.
Well, Minato being the calm and collected type, would probably approach reading Naruto fanfiction with an open mind. He might find some of the stories that depict his heroics in new and interesting ways quite fascinating. Kushina, on the other hand, would be more vocal. She'd either love the fanfiction that shows her as a loving mother and strong kunoichi or be a bit critical if it doesn't match her self - image. For example, if a fanfiction portrays her as too weak, she'd be likely to scoff at it. But overall, they'd both enjoy seeing the different ways the fans have imagined their lives.
It would be very controversial. Fans of the original Naruto series who love the pure and loving relationship between Kushina and Minato would be extremely disappointed. It could also create a lot of negative buzz in the Naruto fan community as it goes against the established characters' personalities.
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.
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.
In a fanfiction, perhaps Minato and Kushina are resurrected during a powerful enemy attack on the village. Naruto is in the middle of the battle when he suddenly sees his parents. At first, he can't believe it. Kushina runs to hug him tightly, while Minato stands there with a proud look. They then join the fight together, using their combined skills to defeat the enemy and have a moment of family reunion.
One possible reason could be a misunderstanding. Maybe Minato thought Kushina had done something to endanger Naruto when in fact she hadn't. In the heat of the moment, he lost his temper and slapped her.
In many Naruto fanfictions, Minato is often portrayed as an even more brilliant strategist and a loving husband. He might be shown using his Hiraishin no Jutsu in creative ways to protect Kushina. For example, in some stories, he uses it to surprise her with little gifts or to show up just in time when she's in danger.
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.