One possible reason could be political. After the war, the villages might be restructuring and Naruto, with his great power, could be seen as a threat. Another reason might be related to the secrets he knows. Maybe some powerful figures don't want him to expose certain things. Also, his Jinchuuriki status could play a role. People might still be fearful of the power within him even after the war.
One possible plot could be that the other villages fear Naruto's power after the war. They put pressure on the Hidden Leaf to banish him. Naruto, feeling betrayed, leaves but then starts to discover new powers or allies in his exile as he tries to prove his worth and find a way back home.
Naruto might initially be shocked and feel betrayed. But he would soon gather his strength. He could use his skills to survive in the wild or in a new land. He would probably keep training to get even stronger.
In such a fanfiction, Naruto might feel extremely betrayed. He's just saved the village in the Fourth War, and being banished would shatter his trust in the village. Maybe he would go on a journey to find his true place in the world, away from the Hidden Leaf.
Perhaps a secret organization within the Hidden Leaf that wants to take over the village. They use Naruto as a scapegoat, getting him banished so they can carry out their evil plans without interference from Naruto. They would be the main antagonists as they are the ones behind the false accusations and the push for his banishment.
It could be some of the traditionalist elders in the Hidden Leaf. They might see Naruto as a threat even after the war, fearing his growing power and influence, and thus engineer his banishment. So they could act as antagonists as Naruto tries to find his place outside the village.
Naruto could also be defiant. Given his strong - willed nature, he might not accept the banishment quietly. He may try to prove his innocence or the importance of his presence in the village. He could use his godlike powers to make a statement, not in a harmful way, but to show that banishing him is a mistake. For example, he might perform some great feats to protect the village from an outside threat even while banished, to show that he still cares about it.
Naruto might also initially feel a sense of abandonment. However, his kind - hearted nature could lead him to try and see the good in the situation. He could start to explore the world outside, learning about different cultures and ninja techniques. He may use this experience to become more empathetic towards others who have also faced hardships, and in the long run, this banishment could be a turning point in his life to become an even greater ninja.
Naruto could also become determined. Since he is 'godlike' in this fanfiction, he might see this as an opportunity to grow even stronger away from the village. He might set out on a journey to master his powers fully and prove himself, with the intention of one day coming back to the village and showing everyone that he was wrongly banished.
In a fanfiction where Naruto is banished, he could end up finding a new village that accepts him wholeheartedly. He might use his skills and experiences to help this new village grow and become a great ninja there. He could also meet new friends and form a new family of sorts, far away from the place that once rejected him.