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 motive could be revenge. Maybe Reid has put away a relative or someone close to the kidnapper in the past. Another motive might be related to Reid's intelligence. The kidnapper could want to use his brainpower for some illegal or self - serving scheme, like cracking a code or coming up with a complex plan.
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.
They'll likely interview people who had recent contact with Reid. The team will also analyze any communication from the kidnapper if there is any. Based on their profiling skills, they'll narrow down the suspects and search for the location where Reid is being held. Morgan might use his combat skills and Garcia will be crucial in providing technological support to find Reid.
It could be an old enemy of Keith's, someone from his past who has a vendetta against him. Maybe a former rival from his days in the military academy who has now turned to more devious means.
In some creative fanfiction, it could be an alternate version of Spiderman himself from a different dimension. This Spiderman has gone bad and kidnaps a fan from our dimension as part of some grand, dark plan that involves crossing dimensions and causing chaos.
A power - hungry nobleman from a neighboring land could be the kidnapper. He might believe that by having Rapunzel in his possession, he can gain some sort of political advantage or use her as a bargaining chip against her kingdom.
It could be Orochimaru. He's always been interested in obtaining powerful individuals for his experiments, and Naruko with her unique abilities would be a prime target.