One idea could be that in the fanfiction, Hinata is under the influence of a powerful genjutsu. This genjutsu makes her see Naruto as a threat to the Hidden Leaf village. So, she betrays him to protect the village in her distorted view. It could lead to a lot of inner conflict for Hinata once she realizes the truth and Naruto having to deal with the pain of her betrayal.
The first consequence could be Naruto's emotional turmoil. He would likely feel extremely hurt and confused, as Hinata has always been someone he trusted. This could lead to him doubting his own judgment in relationships. For example, he might become more guarded in future interactions with others.
In some fanfiction, this could happen due to a misunderstanding. Maybe Hinata is forced into a situation where she has to seem like she's betraying Naruto. For example, she could be blackmailed by an enemy who threatens the safety of the village or her family. Another possibility is that there is some sort of mind - control involved that makes her act against Naruto.
Hinata's betrayal could be a part of a bigger conspiracy. Maybe there are other forces at work in the ninja world that want to bring down Naruto. They use Hinata as a pawn. As the story unfolds, Naruto has to not only deal with Hinata's betrayal but also uncover the conspiracy and save the ninja world from a greater threat.
Naruto might also become more cautious. He's always been a bit of a trusting person, but after Hinata's betrayal, he would be more careful about who he lets close. He would analyze his relationships more deeply and be on guard against future betrayals. This could change his approach to both his friendships and his role in the village as he tries to protect himself from further hurt.
Naruto would probably be extremely hurt. He has always considered Hinata a friend and perhaps more. Betrayal from her would be a huge blow to his trusting nature. He might initially be in denial, not wanting to believe that Hinata could do such a thing.
Naruto would probably be very angry at first. He has always considered Konoha his home and to be betrayed by it would be a huge blow. He might initially try to reason with the villagers, thinking it's a misunderstanding. Hinata, on the other hand, would be more likely to be heartbroken. She's more reserved and the thought of her village turning against her would be deeply painful.
One possible reason could be a misunderstanding. Maybe Hinata is misinformed about Naruto's actions or intentions. For example, she might be led to believe that Naruto has done something harmful to the village when in fact he's innocent.
It could also be a misunderstanding. Hinata might be under some sort of mind - control or false impression. For example, an illusion is cast on her that makes her believe Naruto has become evil. As a result, she takes actions against him that he perceives as betrayal. In this case, once the truth is discovered, they would likely reconcile.
He could be betrayed by a false friend in the DxD world who spreads lies about him. For instance, telling others that Naruto has a hidden agenda to take over their realm.