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.
Yes, there might be such fanfics out there. In the Naruto fandom, with a large number of fans creating various types of stories, it's possible that some would write a story where Naruto destroys Sasuke in a way that could be seen as Sasuke - bashing. However, these kinds of fanfics may not be in line with the overall spirit of the original work which focuses on their complex relationship and growth.
Sasuke might be able to stop Naruto. They have a long - standing relationship and Sasuke has always been Naruto's equal in terms of power. He could use his Sharingan to try and break whatever is controlling Naruto or just fight him head - on and appeal to their old friendship.
His Sage Mode could give him an edge. In Sage Mode, Naruto has enhanced strength, speed, and perception. He could use these abilities to dodge the attacks of the gods and then counter - attack. For example, he could sense the weak points of the gods' defenses and target them with his Rasengan or other powerful jutsu.
It could be an organization similar to the Akatsuki, but with a different goal. Instead of collecting tailed beasts, they are focused on conquering villages. Their army would be made up of powerful and diverse fighters, and Naruto would have to face their leader, who has some sort of special power or ability that makes them a formidable foe.
The theme of justice might be present as well. If 'kina' is something evil or causing harm in the fanfic, Naruto's destruction of it can be seen as an act of justice. Also, the fanfic could explore the theme of sacrifice. Naruto might have to sacrifice something, like his time, energy or even relationships to be able to destroy 'kina' successfully.