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.
Naruto's hatred for the world in fanfiction might also lead to a change in his powers. His negative emotions could either make him lose control of his existing powers or lead to the development of new, more dangerous powers that are fueled by his hatred. This would pose a great threat not only to his enemies but also to those he once considered friends.
It could also lead to some division among the Naruto fandom. Those who support Sakura's view might be more critical of fanfiction, while those who love fanfiction might not like Sakura as much because of her stance. For example, in online Naruto communities, there could be debates and arguments about whether Sakura is right to hate fanfiction.
One consequence could be that fans who really respect Kushina's character might be more hesitant to engage with fanfictions. If they know that Kushina, in a sense, wouldn't approve, they might feel guilty or less interested in exploring those fictional works.
One consequence could be that he leaves the village. He might go off on his own to find a new place where he feels accepted and can start anew.
His relationship with Jiraiya could be affected. Jiraiya has a strong connection with the toads, and if Naruto hates toads, it could create a rift between him and his mentor. This could lead to Naruto losing an important source of guidance and support in the fanfiction.
One possible consequence could be that his relationships with other characters who are related to the Uzamaki clan, like Hinata (since she marries into the Uzamaki family), become strained. It might also lead to internal conflict within himself as he battles with his own identity and heritage.
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 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.
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.
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.