There's no explicit display of his hatred for fanfiction in the official Star Wars canon. However, if we consider his character traits, he was a traditionalist when it came to the Jedi ways. Fanfiction, which often goes against the traditional narrative, would likely be something he'd frown upon. He might have tried to correct those who were spreading false or untrue stories about the Jedi and the Force, which could be seen as a reaction to the kind of things that happen in fanfiction.
It wasn't really shown directly in the movies. But we can assume that if he knew about it, he might have shown his dislike through his actions towards those who misrepresented the Jedi teachings which fanfiction might do.
Since there is no direct showing of Luke hating fanfiction in the Star Wars story as we know it, we can only speculate. Luke was a firm believer in the real Jedi Order and its values. Fanfiction can create alternate versions of events and characters that might go against his beliefs. So, if he were to encounter it, he might show his distaste by distancing himself from those who were involved in creating or spreading it. He would probably be more focused on upholding the true and original Star Wars story and the values it represents.
Often through his internal thoughts. The fanfiction might describe Luke seething with anger whenever he thinks of Vader. For example, in some stories, when Luke is meditating, his thoughts are constantly interrupted by visions of Vader and his past actions, and he can't focus because of his hatred.
The relationships a character has can be a sign of suspect allegiance. If a character has close ties to the enemy side, it could mean they have a hidden allegiance. For example, a character in a Star Wars fanfic who is friends with a lot of Imperial officers while claiming to be a rebel might be suspect. This can lead to a lot of interesting plot twists as the truth is slowly uncovered.
There could be such a fanfiction. Fanfic writers like to explore different facets of their favorite characters. In the case of Luke from Star Wars, his not eating could be a plot device. Maybe he's on a dangerous mission and has no time to eat, or he's in a state of distress and has lost his appetite. This could lead to an exploration of his character, his relationships with other characters who might be concerned about his lack of eating, and how he overcomes whatever is causing him not to eat.
In certain Star Wars fanfictions, the idea of Luke being Rey's father has been explored. This can add an interesting new dimension to the story. It might be because of the way the Force works in the fanfiction universe, or perhaps to create a new family dynamic that wasn't present in the official movies. However, it's important to note that this is only in the realm of fan - created content and not part of the official Star Wars canon.
It could change the way the Rebellion is fought. Ezra's knowledge of certain parts of the galaxy and his connections could be added to Luke's growing influence. This might lead to a more coordinated effort against the Empire. For example, Ezra could inform Luke about some hidden Imperial bases that he discovered during his adventures in the Rebels.
Luke as a spacer in fanfiction can also be a bit of a loner at times. He might prefer the solitude of space travel, using the time to meditate and strengthen his connection to the Force. But when he encounters trouble, he'll step up and use his Jedi skills to protect the innocent. One story could have him coming across a small, defenseless colony under attack by slavers. He would then use his lightsaber and the Force to drive off the slavers and free the colonists.
As they go on adventures together, their bond would strengthen. They could face a great enemy like a powerful dark side user. In the heat of battle, they would rely on each other and start to trust more deeply. Ahsoka might see some of Anakin in Luke, which would make her more protective of him, and Luke would see Ahsoka as a wise mentor figure.
In fanfiction, a 'spacer' Luke Skywalker could be on a mission to spread the teachings of the Jedi across the galaxy. He'd use his starship to journey to various systems, facing challenges from pirates or the remnants of the Empire. His experiences as a spacer would shape him into an even wiser and more powerful Jedi.
One great 'Star Wars Luke Fanfiction' is 'A New Hope: Luke's Journey Beyond'. It delves into Luke's further adventures after the events of the original movie. Another is 'Luke Skywalker: The Lost Years' which fills in the gaps of his unaccounted - for time. And there's also 'Luke's Force Awakening', which imagines his role in the new era of the Star Wars universe.
One idea could be that Luke is sick due to a strange alien virus he caught during a mission. His friends in the Rebel Alliance have to search for a rare antidote while also protecting him from the Empire who might try to capture him in his weakened state.