It could be a disgruntled former crew member. Maybe they were fired from the show and in their anger, they read a lot of fanfiction for inspiration on how to get back at the team. So they plan and execute the kidnapping.
A obsessed fan who has deluded themselves into believing they are part of the Criminal Minds world. They've read so much fanfiction that they think the team members are actually their friends or enemies in this fictional world they've created in their minds, and so they kidnap them to play out some sort of twisted scenario.
It could be someone Reid put away in the past. Maybe a criminal who has held a grudge against him ever since and has now found an opportunity to kidnap him for revenge.
It could be a deranged fan of one of Reid's academic works. This person might have misinterpreted Reid's theories and decided that Reid was some sort of false prophet. So, in his twisted mind, he kidnaps Reid to 'correct' him.
One possible plot could be that a deranged fan, feeling betrayed by the show's direction, kidnaps members of the Criminal Minds team. The kidnapper might demand that the show be brought back in its original format. Another plot could involve a criminal who uses the guise of a fanfiction scenario to target the team, perhaps because they believe the team has wronged them in some way. Maybe a group of obsessed fans accidentally kidnap the team while trying to get an autograph or exclusive access in a really over - the - top and illegal way.
It could be a former criminal that JJ put in prison and who has now been released and seeking revenge. Maybe it's someone from her past that she had a run - in with during her early days in the BAU.
Maybe it's a group of villains working together. They could be from different factions but united by the idea that Izuku has the potential to become a huge threat to their plans. They might kidnap him to either eliminate him or turn him to their side. Also, it could be a lone, obsessed fan of a villain who wants to prove themselves by bringing Izuku to their idol.
A group of outcasts from different islands might kidnap Moana. They feel that they have been wronged by the 'normal' society that Moana represents. They hope that by kidnapping her, they can get the attention they deserve and force the islands to change their ways. But Moana listens to their grievances and tries to find a way to help them while also finding a way home.
It could be Zeref. Since Zeref has an interest in powerful magic users and Natsu is a strong dragon slayer, Zeref might kidnap Natsu to study his magic or use him in some dark plan related to his quest for immortality or power.
It could be a jealous rival from his own village. Maybe someone who is envious of Shikadai's natural talents and popularity, so they decide to kidnap him to get him out of the way.
It could be an envious rival. Maybe someone who's always been in the shadow of Osomatsu and his brothers and decides to take matters into their own hands by kidnapping Osomatsu. Another option is a deranged collector. This person might see Osomatsu as a rare item to add to their collection of oddities. Or it could be a vengeful spirit. In a more supernatural setting, a spirit with a grudge against the Matsuno family could kidnap Osomatsu as a form of revenge.
It could be a rogue werewolf. Maybe this werewolf has a grudge against Stiles' pack and thinks that by kidnapping Stiles, he can get some sort of revenge or leverage.