The first consequence could be a breakdown in the village's unity. Naruto is seen as a hero in Konoha, and if he turns against it, many of his supporters might be confused or even follow his lead. This could lead to internal strife within the village.
One possible reason could be that Konoha has a history of dark secrets. Maybe Naruto and Kushina discovered some unethical practices within the village that made them lose faith in it. For example, the way the village treated the Uchiha clan was quite unjust. Kushina might have known about some of these underhanded dealings and passed on her concerns to Naruto.
Another reason could be that he witnesses corruption or unfairness within the village leadership. If he sees that the system is rigged against certain groups, including himself or his friends, he could grow to hate Konoha and decide to leave.
It could also be due to a lack of support. Naruto was constantly in trouble and trying to prove himself. If his family didn't show up in any way to support him and Konoha didn't do enough to encourage him in a positive way, but rather just punished him for his pranks, he might grow to hate them both.
Well, if Naruto has a bloodline and hates Konoha in a fanfic, it could lead to him becoming an anti - hero. He might use his bloodline powers against Konoha at first. Maybe he teams up with some of Konoha's enemies who share his hatred for the village. This would completely turn the original story on its head.
Some fanfictions have Naruto uncovering dark secrets about Konoha. These secrets could be about the actions of the previous Hokages or the village elders. Discovering these secrets makes Naruto lose faith in Konoha and start to hate it.
It completely flips the original story. In the original, Naruto loves Konoha and eventually comes to terms with his family legacy. But in this fanfic, the hatred changes his character motivation. Instead of striving to protect Konoha, he might be out to get revenge or simply distance himself from it.
The story would deviate from the original themes of unity and friendship. Naruto's hatred could split Konoha into factions. This would mean different training regimens, different missions, and different loyalties. For example, Naruto might start his own group of ninjas who share his views, which would completely change the power dynamics in the village.
One possible reason could be that Naruto might feel overshadowed by the Konoha 12. They all have their own unique skills and family backgrounds. For example, Sasuke is always seen as a prodigy. Naruto, who grew up lonely, could feel a sense of envy or resentment towards them which might be explored in the fanfiction. Also, the Konoha 12 might have some unspoken rules or a clique - like environment that Naruto doesn't fit into, making him develop negative feelings in the context of the fanfiction.
Perhaps Naruto discovers some dark secrets about Konoha that go against his values. Like if the village has been involved in unethical practices that he can't overlook. This could be things like using underhanded tactics against other villages, which would make Naruto, with his strong sense of justice, turn against Konoha.