A college or university can try to punish you for things you say or do on your YouTube channel, but are they in their rights to do so? That's a completely different consideration, a critical consideration, but it is completely different. A school can try to punish you for what you say or post on YouTube. The student does have rights, freedom of speech. It's limited to an extent, but, the student also has an obligation under the school's code of conduct. It depends on what was posted.
If it's racial or sexual or threatening in nature at certain considerations. If it's something that's posted that somebody merely disagrees with and at school is trying to discipline a student for that, is that appropriate? Most likely not. It's going to depend on the specific circumstances at hand. Being accused of misconduct of that nature is serious. It can have profound, short, and long-term consequences. An experienced attorney advisor can help you best understand, navigate the process, and defend against allegations of that nature.