One idea could be that Harry is under a dark spell that makes him kidnap Muggles, but then his friends try to break the spell and save him and the Muggles. Another could be that it's a case of mistaken identity and Harry is wrongly accused of kidnapping Muggles when he was actually trying to protect them from a real threat. Maybe in the fanfiction, Harry kidnaps Muggles to show the wizarding world how wrongly Muggles are treated by some wizards.
In this fanfiction, it could start with Harry having a strange dream that compels him to kidnap Muggles. As he does it, he realizes that there's a hidden message in this act. It turns out that there's a secret group of wizards who are using Muggles in a dangerous experiment. Harry kidnaps the Muggles to protect them from this group. He then has to figure out how to expose this group and return the Muggles to their normal lives without getting caught by the Ministry of Magic, which would surely misunderstand his actions.
Well, perhaps in this 'harry kidnap muggles fanfiction', Harry is being controlled by an ancient artifact. The artifact forces him to kidnap Muggles as part of a dark ritual. His Gryffindor courage still shows through, and he tries to resist as much as he can while his friends scramble to find a way to destroy the artifact. Or it could be that a new dark wizard has framed Harry for kidnapping Muggles to turn the wizarding world against him, and Harry has to clear his name while also ensuring the safety of the kidnapped Muggles.
Maybe Voldemort's old followers who are still up to no good. They might think that by getting Harry to kidnap Muggles, they can bring back the dark days under Voldemort's rule. They could be using some sort of dark magic to influence Harry's actions.
One idea could be muggles discovering a powerful magical artifact and trying to use it against wizards. Another could be wizards trying to hide their world from muggles who have become overly curious due to some strange magical events leaking into the muggle world. A third plot idea might be a group of muggles and wizards teaming up against a common enemy that threatens both their worlds.
One idea could be that Scabior kidnaps Hermione to use her knowledge for some dark wizard's plan. Maybe he's been promised a great reward. Another could be that he mistakes her for someone else at first but then realizes her true value.
Some muggles in fanfiction could be the relatives of a half - blood wizard. These muggles might have a hard time understanding their wizarding family member's abilities at first. They could be initially skeptical or even scared when they witness magic. However, as the story progresses, they might come to accept and even be in awe of the wizarding world.
A simple plot could be that the wizards need a powerful ingredient that only the demigods can provide. So, they kidnap one or more demigods. For example, a demigod's blood might have special properties for a spell.
One possible plot could be that the Avengers mistake Percy Jackson for a dangerous threat. Maybe they've been given false information about his powers being uncontrollable. So, they decide to kidnap him to keep the world safe. But once they have him, they start to realize that he's not what they thought. Percy, being a hero in his own right, tries to convince them that he's on the side of good.
Another concept could be a magical or supernatural 'kidnap love fanfiction'. The kidnapper could be a supernatural being, like a vampire or a werewolf. He kidnaps the human he loves because he wants to protect them from other dangerous supernatural creatures. But the human doesn't understand his motives at first and struggles against him. As time passes, they develop a strange and intense love relationship.
Muggles can be a source of conflict. If a wizard falls in love with a muggle, they have to deal with the secrecy of the wizarding world and potential disapproval from both sides. This can drive the plot in many different directions, like trying to find a way to introduce the muggle to the wizarding world without breaking any rules.
In such fanfiction, Muggles can be shown in different lights. Some portray them as simple and uncomplicated, living their ordinary lives without any knowledge of magic. However, there are also fanfictions where Muggles are more curious or even a bit envious of the magical abilities of Wizards. They might be depicted as trying to find out about the wizarding world despite the secrecy.
One alternative could be a story about the Dragonborn going on a quest to discover their true heritage. They could travel across different lands, meet various characters who help or hinder them in their search for knowledge about their family and their unique powers.