He could also distance himself from them. Naruto might choose to avoid his family, not wanting to be around them as a way to show his anger. He could move out or stop participating in family activities.
His family might have neglected him in some ways. Naruto grew up alone and feeling unwanted in the original story. If in the fanfiction, his family was around but still didn't give him the love and attention he needed, it would be a valid reason for his anger. He has always craved connection and acceptance, and if his family failed to provide that, he would be furious.
He might directly confront her. Naruto is not one to hold his tongue, so he could just barge into Tsunade's office and start yelling about why he's angry. For instance, he could say 'Tsunade - sama, your decision was wrong and it's going to hurt a lot of people!'
If Sakura betrays Naruto's trust in the fanfiction. For example, she might tell Naruto's secrets to the enemy. Naruto has always been very open and loyal to Sakura, so this would be a huge blow to him. His anger would be completely understandable as she would have broken the bond of trust between them.
Another way would be through his actions. For example, if the villagers were being unjust to Naruto, he might start by protecting Naruto more visibly. He could also limit his assistance to the village in other areas until they corrected their behavior. This would be a clear sign of his anger and dissatisfaction with the villagers.
He might lash out with his magic. For example, he could send a spell flying at the source of his anger without really thinking. Sometimes, he just glares intensely, his green eyes filled with fury. And he may raise his voice, shouting at those who have angered him.
One reason could be that Naruto has been through a lot of hardships related to his family in the fanfic. Maybe they didn't support his growth to this godlike state, or they tried to use his power for their own gain. For example, if his family had always been jealous of his potential and when he finally reached this ultimate power, he realized their true nature and decided to cut ties.
Perhaps his family consists of a group of fellow banished ninjas who become his surrogate family. There could be a strong - willed female ninja who becomes his partner, and together they have a child. And also an old sage - like figure who acts as the family's wise elder, guiding them through the difficulties of living in exile.
It could also be due to some family curse or prophecy. In the Naruto universe, there are often strange powers and curses. Maybe there was a prophecy that said Naruto's family had to keep their distance from him to protect him from some greater evil. So, they chose to neglect him in order to keep him safe, even if it was a difficult choice.
One possible reason could be that his newfound 'godlike' powers make his family feel estranged. They might not understand his sudden transformation and the magnitude of his power, which creates a sense of fear or discomfort, leading them to ignore him.
His father, Minato, could be a likely candidate in a really dark fanfiction. Maybe he was resurrected in an imperfect way and his mind was warped, causing him to turn on Naruto.