It might also be related to a prophecy or some dark power's influence. If there was a prophecy that Naruto would bring great destruction, Jiraiya and Tsunade, in an attempt to protect the village, could be misled into betraying him. However, this would be a huge misjudgment on their part as Naruto has always been a protector of the village.
In such a fanfiction scenario, it could be due to a misunderstanding. Maybe there was false information spread about Naruto that made Jiraiya and Tsunade believe he had done something unforgivable. For example, an enemy could have framed him for a major crime against the village.
Another possibility is a misunderstanding. Maybe some false information is spread about Naruto that makes Tsunade believe he has gone bad. In the world of Naruto, there are often enemies who try to create chaos by sowing seeds of distrust. Tsunade, without fully investigating, could fall for such a trick and seem to betray Naruto.
One possible plot could be that Tsunade and Jiraiya are deceived by false information about Naruto. Maybe they are made to believe that Naruto has turned to a dark side. For example, an enemy might have created false evidence of Naruto collaborating with a powerful evil force. Tsunade, being the Hokage, and Jiraiya, Naruto's mentor, would then be forced to take actions against Naruto that seem like betrayal from Naruto's perspective.
He would probably also feel angry. After all, he has sacrificed so much for the village and for them. He might start to question his own beliefs and values. But Naruto being Naruto, he would not give up easily. He would try to prove his innocence and show them that they are wrong. He could go on a journey to find evidence or seek help from other allies who still believe in him, like Shikamaru or Kakashi.
Perhaps the fanfic is exploring an alternate universe concept. In this universe, the relationship between Jiraiya and Naruto has been strained due to different events that didn't occur in the original story. Jiraiya's actions that seem like a betrayal could be a result of different political or personal circumstances in this alternate world. For instance, if there was a power struggle in the Hidden Leaf Village and Jiraiya sided with a different faction for some reason, Naruto would feel betrayed.
He could also try to talk to them directly, despite the betrayal. Naruto has always believed in the power of communication and the bonds between people. He'd want to understand why they thought he was worthy of betrayal and try to convince them that they were wrong.
In such a fanfiction, Naruto might receive more focused training earlier. Jiraiya could pass on his unique ninjutsu skills more intensively, and Tsunade might teach Naruto about medical ninjutsu. Also, Naruto would likely grow up in a more stable family - like environment, with the support and love from both Jiraiya and Tsunade. This could lead to him being more confident and less of an outcast in the village.
In this fanfiction, their relationship would be transformed. They would be like a married couple in a way, but without the formalities. Jiraiya would probably tone down his womanizing ways as he has a family to think about now. Tsunade would be more open and less prickly around Jiraiya. They would bicker less and cooperate more. Their relationship would be centered around Naruto, and as he grows, they would grow together as a family unit, with their bond getting stronger over time.
In some fanfictions, Tsunade might betray Naruto due to political pressure. Maybe the village elders force her hand, believing Naruto's power is too dangerous. It could also be a misunderstanding, like false information about Naruto being a threat to the village reaching Tsunade.
One possible plot could be that Jiraiya is forced to betray Naruto due to some external threat. Maybe an enemy has captured Jiraiya's loved ones and threatened to kill them if he doesn't turn on Naruto. Jiraiya, in a difficult position, might have to pretend to be against Naruto to protect his loved ones while secretly trying to find a way to free both Naruto and his family from the enemy's clutches.
One possible scenario in this fanfiction could be that Naruto grows up with a more balanced upbringing. Tsunade might teach him medical ninjutsu and how to control his emotions better. Jiraiya, on the other hand, would surely train him in powerful combat techniques and in the ways of the sage. Naruto would probably be more mature and well - rounded at an earlier age, with a combination of Tsunade's tough love and Jiraiya's adventurous spirit guiding him.