However, Naruto also has a big heart. In the long run, he would probably try to find a way to save Kakashi or bring him back to the right side. He wouldn't give up on Kakashi easily, believing that there must be some underlying reason for his actions and that he can be redeemed.
At first, Naruto would likely be extremely shocked. He has always considered Sakura a friend and teammate, so this would be a huge blow. He might question his own judgment in trusting her.
One possibility could be a misunderstanding. Maybe Kakashi is framed for something that makes Naruto believe he has betrayed him. For example, an enemy could use a clone of Kakashi to perform a heinous act, and Naruto witnesses it without seeing the full picture.
Naruto would likely be initially shocked. He has always considered the Kyubii as a part of him and a friend in some ways. So the betrayal would be a huge blow to his sense of trust.
At first, Naruto would be completely shocked. He has always seen Hinata as a loyal friend and someone who has deep feelings for him. So the idea of her betrayal would be hard to fathom. He might try to deny it at first.
Naruto might initially try to reason with those who betrayed him. He would want to understand why they did it. But if they refuse to listen or continue to be hostile, he would start to distance himself from Konoha. He could become a lone wolf, using his skills and power to survive on his own while still trying to figure out how to clear his name and get revenge if necessary. He would also likely feel a sense of betrayal towards the friends he thought he had in Konoha.
Naruto would be devastated. He sees Kakashi as a mentor and father figure. He might initially go into denial, not believing that Kakashi would actually abandon him.
Eventually, Naruto could grow resentful. If the ignoring persists for a long time, he might start to think that Kakashi doesn't care about him at all. This could change Naruto's attitude towards Kakashi and might even make him more rebellious in his training or actions. However, deep down, he still probably hopes for Kakashi's recognition and approval.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
Naruto could also feel a sense of confusion. He might wonder what he did wrong or what made Fem Kyuubi choose Sasuke over him. This confusion could lead him to question his own worth and his relationships with others. However, in true Naruto fashion, he would eventually rise above these negative feelings and focus on his goals, like protecting the village and his friends.
Naruto might be initially very disappointed. He has always looked up to Kakashi as a strong and cool ninja, and being refused by him would be a big blow. He could become a bit sulky and withdrawn, feeling like he's not good enough.