I agree that it's overboard on a lot of things, especially in the past couple years, but I think it's important to remember the "cancel culture" started as a way to hold certain people to account who were exhibiting socially unacceptable behavior, but were not being socially punished.
All societies have social norms, and all societies have informal (i.e. not through the legal system) means of enforcing those norms. There was a pretty significant gap in U.S. society's ability to enforce social norms against certain types of people, and social media filled that gap.
Now some people have taken that tool farther than can reasonably be justified, but the best way to fight back against that excess is not to say "cancel culture is oppression!" because it DID fill a need in our society, it DID punish people who deserved to be punished, and I don't think we can get the cat back in the bag. So, don't fight the tool, fight the people using it where it isn't justified.
(Who gets to decide when it's "justified" you ask? Well, we do. As a society. Together, online. We're going to have to figure it out. But if we go into a discussion about cancel culture assuming the other side is only interested in opression, repression, and censorship, it's not going to go well.)