They could also use the idea of being influenced by dark powers. Maybe Naruto comes into contact with a powerful and malevolent force that slowly corrupts him, making him do things that are out of character for the original Naruto. This gives the writer a way to explore a different side of the character while still having a somewhat believable reason for his actions.
Well, often they use the idea of Naruto's strong will. They say that his will is so strong that it breaks the normal limits of what is possible in the Naruto universe. So, his will allows him to access these impossible powers. Also, in some fanfictions, Naruto goes through some extreme and unique training or experiences that no one else has had, and this is what gives him these extraordinary abilities. For example, he might travel to a different dimension where the laws of physics and chakra are different, and when he comes back, he has these new powers.
In certain fanfics, it could be part of a disciplinary system in Hogwarts that has gone awry. The writers might depict a Hogwarts that is more of a strict military - like academy where physical punishment is allowed in extreme cases, and Snape, as a strict teacher, takes it too far. They then use this as a starting point to explore themes of reform in the wizarding school system.
Some writers justify it by creating a situation where Sasuke has to make a great sacrifice. For example, he might give his life to protect Naruto or the Hidden Leaf Village from an overwhelming threat. His selfless act in these scenarios is seen as a way to atone for his past mistakes and show his growth as a character.
Another way is through a series of tragic events. If Naruto experiences multiple losses, such as the death of his closest friends or mentors, he could become disillusioned with the world. Writers can show how this grief and anger transform him into a corrupted version of himself, as he starts to question the values he once held dear.
Fanfiction writers could use power imbalances. If Naruto has suddenly gained a lot of power and doesn't fully control it, he could accidentally hurt Sasuke. It shows the consequences of power and the need for control in their relationship.
In some fanfics, Naruto might be depicted as using excessive force against his friends in a fit of rage. For example, he could accidentally harm Sasuke while they're having an intense argument. This goes against his usual character of valuing his comrades.
They might justify it through misunderstandings. Maybe Arthur is tricked into a situation that looks like cheating but he's really trying to protect Merlin in some convoluted way.
They might justify it through her past traumas. For instance, if Sakura has faced repeated rejections or has been constantly overshadowed in the original story, a writer could use this as a reason for her to betray. She could feel that she has been treated unfairly and that her so - called friends never really understood her pain. So, in the fanfiction, she decides to take a different path that is seen as a betrayal to those around her.
Some writers might justify it by exploring the idea of redemption. They could write Voldemort in a way that shows a glimmer of humanity that Harry, being abused, might be able to relate to on some level. Maybe Voldemort has a hidden past that makes him more complex than just the evil wizard we know.
Some writers justify it by saying that Harry is a descendant of a powerful ancient magical line that was long forgotten. This hidden heritage unlocks his godlike powers as he grows older and discovers more about his past. For example, he might find out that his ancestors made a pact with some powerful magical beings, and the powers are now passed down to him.