Maybe he was blamed for some trouble he didn't actually cause. For example, if something went missing in the orphanage and the caretakers wrongly thought Naruto took it.
Perhaps the other orphans didn't like him and put pressure on the orphanage staff to get rid of him. Naruto was often ostracized in the original story, so this could be a likely reason in the fanfic too. The other kids might have been jealous of the attention he sometimes got, or they might have just been influenced by the general dislike for Naruto in the village.
One possible reason could be his unruly behavior. Naruto is known to be a bit of a troublemaker in the series, always pulling pranks. In fanfiction, this might be exaggerated, and the orphanage might not be able to handle it anymore. Another reason could be that he's suspected of being involved in something dangerous or illegal, even if he's innocent. For example, if there are strange incidents around the orphanage and Naruto is the easy target to blame because of his reputation.
One possible reason could be his prankster nature. Maybe he played one too many harmless but annoying pranks on the staff or other orphans, and they decided they'd had enough. Another reason might be the fear of the Nine - Tails within him. Even if the people in the orphanage didn't fully understand what it was, they could sense something dangerous about Naruto and wanted to distance themselves from him for safety reasons.
Maybe he's falsely accused of stealing important Gryffindor artifacts. For instance, if the Sword of Gryffindor goes missing and Harry is wrongly blamed, the house might decide to kick him out. It could be part of a plot by a jealous student or an outside force trying to disrupt Hogwarts.
Perhaps Naruto's uncontrollable use of the Nine - Tails' chakra endangers the team during a mission. The village leaders see this as a huge risk and order him to be removed from Team 7. Naruto then embarks on a journey to better control his chakra on his own. He might meet some new friends or mentors along the way who help him become stronger and more in control, and eventually, he tries to make his way back to Team 7.
Naruto's view of the world and people around him might change drastically. He was already an outcast, but being kicked out of the orphanage could make him more distrustful. He'll have to learn to fend for himself, which could lead to him developing new skills. For example, he might become better at stealing food to survive, but at the same time, he could also meet some kind - hearted people who will help him and teach him better ways to live.
One reason could be causing disruption. If the 'crusade' involved making a lot of noise, blocking hallways, or disturbing classes, the school would likely take action.
It could also be due to a false accusation. Perhaps someone framed him for something he didn't do, like stealing important artifacts from the school. And in the world of RWBY, if he was found to be secretly associated with a group that the school considered dangerous, that would also lead to his expulsion.
One possible reason could be a serious rule violation. For example, if Harry was wrongly accused of using dark magic within the Gryffindor common room. Another reason might be that he was framed for stealing the Gryffindor sword. It could also be due to a conflict with other Gryffindor students that got out of hand and the house decided they couldn't keep him anymore.
Perhaps she was kicked out due to personal conflicts within the pack. If there were other members who didn't like her or were jealous of her for some reason, they might have spread false rumors or convinced the pack leaders to expel her. It could also be that she was in a relationship that the pack disapproved of, and as a result, they decided to kick her out.
Perhaps Percy was kicked out because of a prophecy that the camp elders misinterpreted. They thought that Percy's presence would bring great danger to the camp, so they made the hasty decision to expel him. It could also be that there was some sort of political intrigue within the camp. Some powerful figures at the camp might have seen Percy as a threat to their power and influence, and so they fabricated reasons to get him kicked out.