He would probably become very distrustful. After all, if your own parents betray you, it's hard to trust anyone else. He might isolate himself from others in the village, thinking that if his parents could turn on him, anyone could.
One way could be that his parents were forced into it. Maybe they were under some powerful dark magic or mind - control that made them seem to betray Naruto. For example, an evil villain could have manipulated them to make Naruto think they don't care about him.
Well, if Naruto was betrayed by his parents in a fanfiction, it would completely shatter his world. He already faced so much rejection from the village. This added betrayal would likely make him more distrustful. He might even turn to the dark side, feeling like there was no one he could rely on. It would be a very dark turn for his character.
His reaction would depend on how the betrayal was presented. If it was a sudden revelation, he would be shocked and devastated. He may start to question his own worth, thinking that if his own parents could betray him, what was wrong with him? He could also become more reckless in his actions, not caring about the consequences as much since he felt like he had already lost the most important thing. This new Naruto could also be more empathetic towards the villains in the story, understanding their feelings of being wronged or betrayed in some way.
In a fanfiction where Naruto is betrayed by his parents, the implications are vast. Firstly, Naruto's motivation which was previously driven by a desire to gain recognition, including from his absent parents, would be turned on its head. He may no longer strive for the same things. His relationships with his mentors like Iruka and Kakashi could also be affected as he struggles with this newfound sense of abandonment. Moreover, the village's perception of him might change as he becomes more bitter. This could lead to a split in the village, with some supporting Naruto in his new, darker path and others trying to bring him back to his former self.
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.
In some fanfictions, it could be due to a long - hidden family secret. His parents might have had a past that they were ashamed of or a debt they had to pay, and unfortunately, Harry became a part of that repayment which led to the perception of betrayal. They could have made a deal with a dark force before Harry was born, not realizing the full implications it would have on their son.
In such a fanfiction, perhaps the parents were forced to betray Harry due to some dark magic or a powerful enemy threatening them. Maybe they had to give up Harry to save the wizarding world from an even greater evil.
In a more complex scenario, Naruto could be influenced by an outside force. Let's say an enemy of Konoha uses mind - control or some form of manipulation on Naruto. They make him believe that the ANBU is the enemy of the village and that he needs to take them down. As he betrays the ANBU, he slowly starts to realize that he's been used, but by then he's already in too deep and has to find a way to fix the situation and regain the trust of his friends and the village.