For Naruto, his view of Kakashi would also change. He wouldn't have that mentorship within the context of Team 7. He might resent Kakashi at first for allowing him to be removed from the team. But as Naruto grows on his own, he might come to see Kakashi in a new light, perhaps as a potential ally rather than a former sensei. And Kakashi, on his part, might start to regret his decision to remove Naruto from the team as he sees Naruto succeed without his guidance.
The relationship between Sasuke and Sakura would change significantly. Without Naruto as a buffer, they might have a more strained relationship. Sasuke could become even more aloof, and Sakura might struggle to understand him without Naruto's positive influence. Also, their team dynamic would be completely different, and they might not grow as much as they did in the original story.
One possible plotline could be Naruto feeling a great sense of betrayal. He might go off on his own journey to become stronger in a different way than in the original story. Maybe he meets new allies who help him discover new powers or techniques.
The relationship between Naruto and Sasuke could become more complex. If Sasuke's future self has accomplished great things but at a cost, Naruto might question his own ideas of success. For Sakura, seeing her future self might make her more assertive in her relationship with the boys, especially if she has become a very respected ninja.
Sasuke and Sakura's relationship would be different. Without Naruto as a buffer, they might have a more strained relationship. Sasuke could be more focused on his own goals and less patient with Sakura. Kakashi's relationship with the team would also change. He wouldn't have Naruto's unique brand of enthusiasm to deal with, so he might be more strict with Sasuke and Sakura.
His relationship with Sasuke might become more complicated. Since Sasuke is an Uchiha and Naruto now has an Uchiha - like power through the transplanted eye, Sasuke could be jealous or feel that Naruto is encroaching on his family's legacy. On the other hand, it could also bring them closer as they now share a similar power source.
His relationship with the Leaf Village would become more personal. He'd be part of the Sarutobi clan in a sense. His bond with Shikamaru and Choji would strengthen as they are Asuma's students. Naruto would also have a new father - figure relationship, which would change how he views authority.
In terms of his relationship with the villagers, those who once bullied him for being an orphan and having a different look (with his blond hair) might be even more hostile if his red hair makes him stand out more. However, there could also be some villagers who see his red hair as a sign of something special and start to respect him more, which could lead to a shift in how Naruto views the village and his place in it.
His relationship with Sakura would change a lot. Sakura might be more protective of Naruto as a cat, seeing him as a cute and vulnerable creature. She might take on a more motherly role towards him. With Kakashi, Kakashi would probably be amused by Naruto's cat form at first, but then he'd start to worry about how to turn him back. And as for his friends in general, they'd have to communicate with him in different ways, like through body language and meows.
His relationship with Sasuke would be greatly affected. Sasuke might see Naruto as a completely different person now that he has become the Nine - Tails. There could be a sense of fear or at least a new level of caution from Sasuke. They might have to re - establish their bond, as Naruto's new form could be a threat in Sasuke's eyes.
Naruto's relationship with the younger generation would be very different. As a Jounin, he would be a role model. The kids in the village would look up to him even more. He could inspire them to work hard. His relationship with Hinata might also evolve. Maybe he would finally have more time to focus on their relationship now that he has achieved a higher rank and more stability in his ninja career.
Their relationships with their friends would become extremely strained. Their former comrades would be shocked and saddened by their turn to evil. Naruto and Hinata would no longer be seen as the heroes they once were, and their friends would likely try to bring them back to the light, but it would be a difficult and dangerous task.