It could be that the crossovers in Fairy Tail fanfic often misinterpret Naruto's character. Writers might not capture his essence accurately, making him act out of character in the context of a Fairy Tail - Naruto mash - up. This could lead to Naruto, as a character concept, seeming to 'hate' these fanfics as they don't do justice to who he is.
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 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.
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.
Well, in fanfics, sometimes authors like to take a completely different approach to characters' relationships. In the case of Naruto hating Kushina, it could be related to a power struggle within the fanfic's plot. Maybe Kushina has some power that Naruto feels threatened by, or there are political or family reasons within the made - up world of the fanfic that cause this animosity. It's all about exploring new and unexpected ideas in the world of fanfiction.
In some fanfics, Naruto might hate Tsunade due to her decisions regarding the village. For example, if she makes choices that Naruto believes put the younger generation at risk or if she is too strict with the shinobi training policies. Naruto, being someone who values his friends and the future of the village, could grow to dislike her.
Maybe in the fanfic, Kurenai has some actions that conflict with Naruto's beliefs. For example, she might oppose Naruto's way of handling certain village matters.
Maybe he just doesn't like the way some fanfirls act in the fanfic. They might be too obsessive or change his character in ways he wouldn't like.
In some fanfics, Naruto might be made to hate the village because of how he was treated as a child. He was ostracized and shunned by many villagers due to the Nine - Tails sealed within him. This constant rejection could build up resentment over time in a fanfic - based scenario.
In some fanfics, Naruto might seem to 'hate' family due to various reasons. Maybe the author wants to explore a different side of his character. For example, if the fanfic has a plot where his family has wronged him in some way, like his father not being there for him during his difficult childhood. However, this is not the typical view of Naruto in the original series, where family is something he longs for.
In some fanfics, Naruto might be made to hate Kami due to a misinterpretation of Kami's role. Maybe the author wants to create a new narrative where Naruto rebels against the traditional concept of Kami in the Naruto universe.
Another reason could be related to his origin. In fanfic, if his Uzumaki heritage is explored in a way that makes him feel like a burden or an outcast more than in the original series. Maybe there are secrets about his family that make him question his own worth. For instance, if there are made - up prophecies or family curses in the fanfic that make him think he's doomed to bring misfortune, he could end up hating himself.