Another idea is that Naruto has to go through some extreme emotional turmoil which unlocks a hidden potential within him. We know from the original series that his emotions can often fuel his power. So, if something really tragic or inspiring happened, like the threat of total annihilation of the ninja world, he could break through his limits and gain the power to destroy the moon.
The tides would be severely affected. Since the moon has a gravitational pull on the planet, without it, the oceans would become very unstable. Coastal areas would experience massive floods and then receding tides like never before, which would disrupt fishing and coastal communities.
It could be Sasuke. If he were to turn to the dark side in the fanfiction, his Rinnegan powers could be used to destroy Konoha. He has the potential to be extremely powerful and if he has some sort of vendetta or is influenced by some dark force, he might take his anger out on the village.
Madara Uchiha could also be a possible antagonist in this scenario. Even if he is dead in the original story, in a fanfiction, his lingering influence or a resurrected form could manipulate Naruto. Madara was always against Konoha's ideals to some extent and might use Naruto as a tool to destroy what he hated.
Well, it could be due to a plot twist in the fanfiction. The author might want to show Naruto's growth in a more extreme way. Naruto could have received some special training from an unknown source that gives him an edge over Neji. He might also be under the influence of a special power - up item or a curse that enhances his abilities but also makes him more violent. In that case, his strength could easily overpower Neji's skills.
One possibility could be that Naruto is somehow transported to the world of Greek mythology where Olympus exists. Maybe his powerful jutsu are seen as a threat to the gods on Olympus. He could start by accidentally causing chaos in a nearby village which gets the attention of the minor gods. As they try to stop him, he realizes he has to fight back to protect himself and in the process, his attacks end up targeting Olympus.
Maybe Naruto gets some sort of dark power that makes him go berserk and start destroying everything in his path. For example, he could be influenced by an ancient evil curse.
It could be a new character that we haven't seen in the original Naruto series. This character might be jealous of Naruto's power and wants to see him destroy his own world so that he can take over the chaos that follows.
In this fanfiction scenario, Naruto might be able to destroy Sasuke during the Chunin Exams due to his own growth and newfound abilities. Maybe he has mastered a new jutsu that gives him an edge over Sasuke. For example, if Naruto has fully harnessed the power of the Nine - Tails at this point, his strength could be overwhelming.