When fanfiction alters Naruto's goals and values. Naruto in the original series has strong beliefs in friendship and protecting the village. If in fanfiction, he abandons these values for personal gain, it is a form of betrayal. This can happen when authors in fanfiction want to create a different kind of story without fully respecting the integrity of the original Naruto character.
By changing his personality completely. For instance, if fanfiction makes Naruto into a coward when he is known for his courage in the original.
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.
Initially, Naruto would be heartbroken. His friends and his village mean everything to him, and the thought that the gods, who are supposed to be just, have turned against him would be a huge blow. However, he wouldn't give up. He would use his determination and his unwavering belief in himself. He might start looking for allies among those who are also disillusioned with the gods or who believe in his innocence.
At first, Naruto would be extremely hurt. He has always considered Team 7 as his family, so their betrayal would be a huge blow. He might go into a state of shock and disbelief.
He might be initially shocked and heartbroken. Naruto has always valued his friends and the village's trust, so when that's suddenly taken away, he's in disbelief. He could try to reason with his friends at first, but when they don't listen, he might become angry and determined to prove his innocence on his own.
Naruto could also feel a deep sense of hurt. After all, he has been through a lot with Sakura. In the face of her betrayal, he might start to question his own judgment of people. However, being Naruto, he would not give up easily. He might try to find a way to redeem Sakura or at least make her see the error of her ways. He would draw on his own experiences of being ostracized in the past and use that to try to understand her actions and find a solution.
Naruto would be determined to get to the bottom of it. He would not just accept the betrayal at face value. He would use his skills and the help of his friends to investigate what made Jiraiya turn against him. Naruto's ninja way is about never giving up, and this situation would be no different. He would fight against this betrayal, both physically if Jiraiya became an enemy in combat, and emotionally, trying to understand the reasons behind it all while still holding on to the hope that Jiraiya could be redeemed.
He could also feel angry. After all, he has fought for his friends and the village. To be betrayed by someone like Sirzechs would make him want to prove his innocence. He might start training even harder to show that he is not the bad guy Sirzechs is making him out to be. And he would likely try to find evidence to clear his name.
Naruto would be extremely hurt. He's a very emotional person who values friendship deeply. He'd probably first try to understand why Yugao did it. He might be in denial at first, thinking it's some kind of misunderstanding.
Naruto might initially be in shock. He's a person who values friendship highly, so being betrayed by Mirajane would be a huge blow. He'd probably first try to talk to her, to understand why she did it.
Naruto would probably be extremely hurt. He has always looked up to the Sandaime as a grandfather figure. So, he might initially go into a state of shock and disbelief.