He would likely be seen as a traitor by the village. The villagers, who once saw Naruto as a hero - in - the - making, would now turn against him. He'd be hunted by the ninja forces of Konoha.
The concept of Hokage Naruto killing Sasuke goes against the essence of their relationship in the original series. Naruto has always been striving to save Sasuke, to bring him back to the right path. However, in some very niche and edgy fanfictions, this might be explored. But overall, it's not something that is widely embraced. The Naruto fanbase generally gravitates towards positive resolutions of their relationship.
Perhaps the Hokage has made a decision that Naruto believes will destroy the village's future. Like if the Hokage decides to sacrifice a large number of innocent villagers in order to achieve a short - term goal. Naruto, with his strong sense of justice, might see killing the Hokage as the only way to stop this madness.
One possible consequence could be chaos. Naruto was often seen as a symbol of hope and peace. His death at the hands of Madara would likely shatter the dreams of many characters. The villages might descend into fear and distrust again, and there could be a power vacuum that leads to wars between the different ninja villages.
The Akatsuki would surely be affected. They would lose one of their members, which could disrupt their plans. Also, it might change the way other characters view Naruto. Some might see him as a more formidable threat, while others might see him as a hero for taking out a dangerous enemy.
One consequence could be a shift in the power balance in the ninja world. If Naruto kills Hanzo, the village that Hanzo was protecting or ruling might be thrown into chaos. His death could also lead to his followers seeking revenge against Naruto or his village.
The most obvious consequence would be chaos. Naruto was the hope for the village. His death would likely lead to a great sense of despair among the villagers. Konoha might lose its strength and confidence.
A major consequence is how other characters react. The village elders might treat him differently, perhaps with more reverence or more suspicion. Also, his enemies might see him as an even greater threat. Naruto himself might also feel a greater sense of responsibility towards the village, as he is now connected to its founder in a very special way. This could lead to him making different decisions in battles and in the overall story arc.
If Sasuke kills Naruto in fanfiction, it could lead to chaos in the shinobi world. Naruto is seen as a symbol of hope and peace, so his death would shatter the dreams of many. Villages might start to distrust each other more, and there could be a power struggle as no one as unifying as Naruto is around.
The most immediate consequence would be a huge blow to the morale of Konoha. Naruto is like a symbol of hope. His death would likely make the villagers feel very vulnerable.
Well, it depends on how it's written. If it's just for shock value, it might not be a very good fanfic. But if the author has a well - thought - out plot that explains Naruto's actions, like if the Hokage has been secretly evil all along and Naruto discovers this and has to take drastic action, then it could be an interesting take. However, it's still a very controversial concept within the Naruto fan community.