One possible scenario in such a fanfic could be that Naruto is betrayed by his new comrades in the DxD world. Maybe they misunderstand his motives or are jealous of his power. For example, they might think he's using his abilities for his own gain rather than the common good.
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.
It could be Zabuza. He might pretend to be on Naruto's side at first during the Wave events and then betray him when Naruto least expects it. Zabuza is a mercenary and his loyalty can be easily swayed.
Naruto would be deeply hurt. He would probably feel a mix of anger and sadness. At first, he might try to reason with Tsunade, to find out why she betrayed him.
At first, Naruto would be shocked and confused. His world view would be shattered. But then, he would draw on his inner strength. He has overcome so many hardships before. He might feel a deep sadness, but also a sense of resolve. He would still believe in the power of love and friendship, and use that to face Kushina's betrayal. He could also use this experience to grow even stronger and more determined to prove himself and his beliefs.
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.
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.
Maybe the gods are jealous of Naruto's ability to inspire people. In this fanfic, they could use their divine powers to make it seem like Naruto has committed heinous crimes. His village would turn on him, and he'd be on the run. Along the way, he might discover some ancient power that can counter the gods' treachery and use it to clear his name and get revenge on those who wronged him.
In such a fanfic, Naruto might become extremely bitter. He could lose his positive attitude and turn against the village that once shunned him. Maybe he would seek power elsewhere, perhaps from darker sources.
One possible plot could be that Tsunade is misled by false information about Naruto. Maybe some powerful enemy fabricates evidence that Naruto is a threat to the village. Tsunade, believing this, exiles Naruto. Naruto, feeling betrayed, then has to prove his innocence while also facing external threats.