She might be disappointed at first. Since she is interested in Naruto, she may have been curious about the fanfiction as well. But being the obedient daughter she is, she would probably respect her father's decision.
Hinata might initially be confused as to why her father is so against Naruto fanfiction. But after some thought, she would realize that Hiashi is probably trying to protect her in some way. She may then find other ways to explore her love for Naruto, such as studying the different fighting styles in the official story or collecting Naruto - related merchandise instead of reading fanfiction.
In some fanfictions, Naruto might use his newfound jutsu skills. He could quickly dash in between Hiashi and Hinata, using his speed and agility to block any attacks Hiashi might be launching towards Hinata. His Rasengan in his hand, ready to defend if Hiashi doesn't back down. This shows Naruto's determination to protect Hinata from any harm, even from her own father in this fictional scenario.
However, Naruto is also a very loyal and understanding person deep down. So after the initial shock and anger, he would probably start to investigate the situation more. He might talk to their friends like Shikamaru or Sakura to see if they know anything. He would want to get to the bottom of it rather than just making a hasty judgment.
Hiashi could be initially skeptical. Naruto has a reputation for being a bit of a troublemaker at times. But if Naruto presents a good case, Hiashi might warm up to the idea. For instance, if Naruto shows how his actions would bring honor and prosperity to the Hyuga clan.
Well, their friendship is like a foundation. Naruto, having known Hinata for a long time, values her. In the situation where he has to save her from Hiashi, his friendship is what pushes him to put himself in harm's way. He remembers all the times they've shared, the support Hinata has given him in the past. This makes him determined to return the favor and protect her. It also means he's more likely to understand Hinata's perspective and try to resolve the issue between her and Hiashi in a way that benefits her in the long run.
Maybe Hiashi thinks Naruto fanfiction might contain inappropriate or untrue portrayals of the Naruto world and characters. He wants to protect Hinata from being influenced by such potentially inaccurate or improper content.
He could be surprised and happy.
Hinata might be very cautious at first. She has been deeply hurt by Naruto's cheating, so even though he regrets it, she would need time to heal. She may not immediately forgive him and might keep her distance to protect herself.
Hinata might also be determined to prove her innocence or change Naruto's mind. She could start on a journey to find out the real reason behind her banishment and clear her name. She may gather allies and evidence to show Naruto that he has been misled.
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 might convince Hiashi by pledging his loyalty to the Hyuga clan. He could say that he'll uphold the clan's values and traditions. Also, Naruto could mention how Hinata has been a positive influence on him, which shows his respect for her. He might also talk about his plans for the future and how Hinata will be an important part of it in a way that benefits both the Uzumaki and Hyuga clans.