Maybe Naruto hates Fairy Tail fanfic because the two universes have very different themes and power systems. Naruto's world is more about ninja skills, clan politics, and personal growth within a set ninja framework. Fairy Tail is about magic guilds and more flamboyant magic use. The clash of these different concepts in a fanfic might be unappealing to Naruto fans who prefer the purity of the Naruto universe.
Perhaps the art styles play a role. Naruto has a distinct art style that some people are really drawn to, and when they look at Fairy Tail, they just don't like the visual aspect as much. Also, the story themes in Naruto are often darker and more about political intrigue and personal sacrifice, while Fairy Tail is more about friendship and adventure. Fans of Naruto's darker themes might not like Fairy Tail's more upbeat nature.
The power scaling might be another issue. Naruto has a very detailed and complex power system that is based on chakra, jutsu, and ninja ranks. Fairy Tail has its own magic - based power system. In fanfics, getting these power systems to mesh well can be difficult, and Naruto might 'hate' being part of a poorly - balanced power - system fanfic.
On the positive side, it could inspire some fans to try and bridge the gap. There might be some fans who see this divide and try to find common ground between Naruto and Fairy Tail. They could create fan works that combine elements of both in a positive way to try and change the negative perception.
There might be a lot of bad writing in the fanfiction that involves Natsu. Poorly written dialogue, actions that don't make sense for his character, or just a general misrepresentation. If the fanfiction is full of these elements, it could give the impression that Natsu hates in that fictional world created by the writer, even though it's not true to his real character.
Perhaps in the fanfiction's plot, Natsu makes a big mistake that endangers Lucy or her friends. Let's say he recklessly takes on a powerful enemy without a proper plan, and Lucy's friends get hurt as a result. This might cause her to hate Natsu for his irresponsible behavior.
In that fanfiction, it might be designed that way. Naruto has incredible powers in his own series, like his various jutsu. If translated into the Fairy Tail world in fanfiction, his skills could potentially make him very powerful. But it also depends on how the author of the fanfiction interprets and balances the power systems of both universes.
The Sharingan in such a fanfiction could be used as a tool for a Fairy Tail character to gain an edge in their battles. They might initially struggle to control it, but as they learn more about it, they become a formidable force. For instance, they could use the Sharingan's genjutsu abilities to deceive opponents in the Fairy Tail battles.
In a fanfiction, there could be a situation where Lucy is forced to side with a group that Natsu is against. This would make Natsu see her as an enemy. Or perhaps there is a prophecy that Lucy is involved in that Natsu misinterprets as something bad. He might think she is a threat to the guild or his friends. Also, if there is a love triangle situation where Lucy chooses someone else over Natsu in a way that really hurts his feelings, that could be a reason for him to start hating her.
In the Fairy Tail world, Naruto would bring his unique ninja abilities. For example, his shadow clone jutsu could be used in creative ways during battles or to perform tasks. He would likely befriend Natsu because they both have a passion for fighting and protecting their friends. Naruto could also introduce new combat styles to the Fairy Tail guild, which might change the way they approach battles.