Once he realizes it's true, he would be deeply hurt. Naruto has a big heart, and being betrayed by someone he cares about would cause him a great deal of emotional pain. He might become angry and feel a sense of betrayal that could fuel his desire for revenge against whoever made Hinata do this.
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.
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.
He would be filled with rage. Naruto has a strong sense of justice and the fact that someone took Hinata away from him would fuel his anger. He would vow to find and punish whoever was responsible. He might even become reckless in his pursuit of vengeance, endangering himself and those around him. His friends would have to step in to try and bring him back to his senses.
Naruto would probably be heartbroken. He loves Hinata deeply, so finding out she might have cheated would shatter him.
Hinata might be shocked at first. She has always adored Naruto, and this sudden act of aggression from him would leave her stunned and unable to process it immediately.
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.
Naruto, being the energetic and battle - loving guy he is, would likely be on the edge of his seat, eager to see who comes out on top in each death battle. He might be making bets with himself about the outcomes. Hinata, with her gentle nature, would be a bit more subdued. However, she would also be intrigued. She might be more concerned about the safety of the fighters, even though it's just a fanfiction battle. And when a fight gets really intense, she might clutch Naruto's arm without realizing it, while Naruto is too engrossed in the action to notice at first.
Hinata would likely be conflicted. On one hand, she still has feelings for Naruto, but on the other hand, she can't tolerate his arrogance. So, she would start by observing him from a distance. As she notices how his arrogance is affecting others, she would gather the courage to approach him. She would tell him how his actions are not in line with the values he once held dear, like friendship and protecting the weak. And she would hope that her words would make him reflect on his behavior.
At first, Naruto would be stunned. But being Naruto, he'd quickly gather his wits. He'd probably joke around a bit to lighten the mood and try to get Hinata to open up. When he realizes she's serious, he'd start to analyze the situation. He'd think about what could have made Hinata do this and try to find a solution that would not only free him but also help Hinata if she's in some sort of trouble. He might also think about how this would affect their friends and the village as a whole.
Naruto would probably be shocked at first. He might not have expected Hinata to leave him for Kiba. He could be angry at himself for not noticing Hinata's unhappiness sooner.