In some fanfictions, Sakura may make decisions without considering Naruto's opinion. Naruto values his friends and their input, so if Sakura goes ahead and does something like endangering the team or making a big decision on her own that affects everyone, Naruto could get mad. Also, if Sakura were to insult Naruto's dream of becoming Hokage, that would definitely be a reason for his anger as that dream is very important to him.
One possible reason could be if Naruto in the fanfiction is being unfaithful to her. In the original series, their relationship is built on trust and love. So, if the fanfic portrays Naruto in a way that goes against that, Hinata might get mad.
In some fanfiction scenarios, if Nami were to side with an enemy, even if it was for a seemingly good reason like trying to protect the crew in a way that Luffy doesn't understand. Luffy has a strong sense of loyalty to his crew and seeing Nami on the 'opposing side' might enrage him. He might feel betrayed and his anger would be a natural reaction.
One possible reason could be if Katsuki is rude to Izuku. Since Inko is Izuku's mother, she would naturally get mad at someone who is mean to her son. For example, if in the fanfiction Katsuki makes fun of Izuku's dreams or abilities in a particularly cruel way in front of Inko, she would likely become angry.
Well, it might be that the fanfiction focuses too much on Sakura in a way that Naruto feels is unfair to the other characters. Naruto is part of a big world with many important people, and if the fanfic just hones in on Sakura all the time, he could get fed up. Also, if the fanfiction has Sakura constantly putting Naruto down or not appreciating his efforts like in the real story, that could be a reason.
Perhaps in the fanfiction world, there is some sort of magical or technological device that mutes Naruto. This could be part of a plot where an enemy uses this device to stop Naruto from using his inspiring speeches or to isolate him from his friends. By muting him, they can disrupt his normal way of communicating and leading, which is a key aspect of his character.
Maybe Tails was tinkering with Sonic's shoes or some other personal item without permission. Sonic values his stuff and his independence. If Tails was messing around with his things in an attempt to 'improve' them but instead caused a problem, Sonic would likely be angry.
Maybe Chi - chi is constantly comparing Gohan to Goku in the fanfiction. Gohan has his own identity and abilities, and being compared all the time can be frustrating. He could get mad because he wants to be recognized for who he is, not just as Goku's son. Also, if Chi - chi is interfering too much in his training or friendships, that could also lead to his anger.
Perhaps Percy forgets an important promise he made to Annabeth. In their relationship, promises are significant. If he fails to keep one, like a promise to help her with a project or be at a certain place at a certain time, Annabeth would surely be mad. It could also be that Percy accidentally breaks one of Annabeth's creations or possessions, which she holds dear.
In the fanfiction, if someone were to insult his dueling skills or question his abilities, that would probably make Zane mad. He takes his dueling very seriously and has a lot of pride in his skills. So any slights towards his dueling capabilities could set him off.
One possible reason could be training. Maybe Kakashi's training methods are too harsh for Naruto. Naruto is eager to become stronger quickly, but Kakashi might be holding him back in Naruto's eyes. For example, Kakashi could be making Naruto do repetitive basic drills instead of teaching him more advanced jutsu right away.