It could be Orochimaru. He's always been interested in Naruto's power, especially the Nine - Tails within him. He might have come up with a new devious plan to capture Naruto and use his power for his own dark experiments.
Voldemort's remaining Death Eaters could be behind it. They might see Hermione as a threat to their attempts to regain power in the wizarding world.
It could be the Kara organization. They've been shown to be interested in Boruto's Karma mark in the original series, so they might have finally made a move to abduct him in the fanfic.
Another plot could be that Naruto goes missing because he's on a self - imposed exile. He might feel that he's putting his friends and the village in danger due to some new power he discovers within himself that he can't control. So, he decides to disappear to protect everyone.
It could be a former Leaf Village ninja who left due to some sort of disagreement. Maybe someone who didn't agree with the village's leadership or its way of training young ninjas.
One great source for Naruto and Hinata fanfiction could be FanFiction.net. You can search for stories specifically focused on their relationship there. There are often new and interesting takes on their story, from how they first fell in love to their married life in the future.
Definitely the Giants. They have a history of causing trouble for the demigods. Annabeth's disappearance could be part of their plan to weaken the demigod forces. They might think that without Annabeth, the demigods would be less organized in their battles.
Madara Uchiha could also be a likely cause. If he somehow managed to return or had a long - planned scheme that involved breaking Naruto's sanity. He was a very powerful and devious foe who could use his knowledge of the ninja world and its powers to target Naruto's mental stability.
It could be Orochimaru. He's always been interested in power and experimenting. Maybe he sees Naruto as a perfect guinea pig to test some new jutsu that goes horribly wrong and causes Naruto to explode.
The Akatsuki could be antagonists. Even if they were defeated in the original story, in the fanfiction they might have a new plan and have kidnapped Naruto for some reason related to the tailed beasts. For example, they might want to use his Nine - Tails chakra to revive a powerful member or complete a dangerous jutsu.
Kimimaro could be an interesting missing nin character to explore in fanfiction. He was a tool for Orochimaru, but had his own internal struggles. You could write about his life before fully becoming a missing nin, his loyalty to Orochimaru despite his own deteriorating health, and what might have happened if he had broken free from Orochimaru's control. Another character could be Nagato. Before he became Pain, he had experiences that could be considered as leading towards a missing - nin - like existence. His views on peace and his use of the Akatsuki could be delved into in the context of a missing nin story.