A common theme is the clash of different power systems. For example, when Shinobu crosses over into a world like 'Fullmetal Alchemist', her demon slaying powers contrast with the alchemy in that world.
Well, Mikey might be a bit surprised at first. He would probably be intrigued by the different scenarios the fanfiction presents about Takemichi. Draken, on the other hand, might be more critical and analyze how the fanfiction portrays Takemichi's growth and relationships. Mitsuya could find it interesting from an artistic point of view, seeing how the writer has used Takemichi's character to create new stories.
One popular 'shinobu kocho crossover fanfiction' is the one where she crosses over with the world of 'Harry Potter'. In this fic, Shinobu's skills as a demon slayer are put to the test in the magical world. She might have to face new types of 'demons' in the form of dark wizards.
Some characters might become more protective of Takemichi if the fanfiction shows him in a difficult situation. They would feel a stronger bond towards him, wanting to ensure his safety. However, if the fanfiction distorts Takemichi's character too much, it could cause some confusion and even a bit of a rift. They might start to question if they really know Takemichi as well as they thought.