He might use his influence as a hero. Naruto has a lot of friends and supporters in the village. By getting them to see his point of view about the council's inefficiencies or wrongdoings, he could start a movement to oust the council. For example, he could talk to his old friends like Shikamaru, who is intelligent and might be able to come up with a strategic plan.
Well, it could be that the civilian council has always been opposed to Naruto's ideas of bringing change to the village. Naruto might have some revolutionary plans for the Hidden Leaf in the fanfic, like making it more inclusive and less hierarchical. But the civilian council, being the conservative force, tries to block his every move. This constant opposition and their attempts to undermine Naruto's efforts would make him hate them. For instance, they could have vetoed any proposals Naruto made regarding better treatment for orphans or outcasts in the village, which Naruto, having been an orphan himself, would find deeply offensive.
One possible reason could be that the council often restricts Naruto's actions. They might see him as a potential threat or a wild card due to his Nine - Tails power. So, Naruto, being a free - spirited person, would naturally hate being controlled by them.
Naruto could also show his hatred through his actions. Maybe he refuses to cooperate with any mission or task that is directly related to the council's orders. He would rather do things his own way or follow the orders of someone he trusts more, like Kakashi or Iruka.
On the positive side, new and better policies could be implemented. If the old council was corrupt or stagnant, getting rid of them would open the door for fresh ideas and reforms. Naruto could bring in new people with different perspectives to help run the village, leading to a more prosperous and fair Konoha.
Some of the elders in the council are also very hated. They are usually portrayed as being old - fashioned and stubborn. They oppose any new ideas or changes that could potentially disrupt the status quo in Konoha. Their lack of understanding of the younger generation, like Naruto's generation, and their reluctance to adapt to new threats make them disliked in these fanfictions.
I think some of the younger ninjas in the village would support Naruto. They look up to him as a role model. Also, those who have been helped by Naruto in the past, like the families of the villagers he saved. They would see that Naruto is fighting for what's right and would stand with him against the council. Additionally, some of the outcast ninjas who feel oppressed by the council's rules might also join Naruto.
In some fanfiction scenarios where Naruto kills the civilian council, it might be seen as a reaction to years of mistreatment and oppression. The civilian council in the Naruto universe has often been shown to be short - sighted and discriminatory towards Naruto. However, from a moral standpoint in the real world, killing is never an easy solution. But in the context of a fictional and often corrupt world of Naruto fanfiction, it could be a way to show Naruto breaking free from the chains that have held him back for so long.
In some fanfictions, Naruto might use his unexpected knowledge. For example, he could have learned about some ancient ninja tactics that the council overlooked. He then uses this knowledge to solve a problem or make a plan that the council couldn't come up with, thus outsmarting them.