Consider how you might think differently if it were people facing unwanted negative consequences of actions or expressions that conservatives disagreed with.
When CPAC de-platformed Milo Yiannopoulos and Young Pharaoh, weren't they being canceled? Yet I have no problem with them doing that.
Whenever I try to come up with a non-partisan definition of "cancel" - one that doesn't explicitly point to "liberals" or "left" - I easily discover that of course conservatives also cancel.
Because facing negative consequences of actions or expressions is part of human nature.
Now, of course there are times when I think that the "canceling" was wrong. If someone loses their job because of their support for unionizing, or faces pressure to suppress reporting sexual harassment, then that's both canceling and illegal, and I am definitely against both cases.
My problem is that "cancel" seems to have a built-in anti-left bias, making it simply a proxy for "leftists should stop complaining."
The point is, there is always someone trying to push things one way or another, and up until about 20 years ago, it seemed like things always found their way to an equilibrium...
My how things have changed.
https://en.wikipedia.org/wiki/Cancel_culture gives example definitions:
"to stop giving support to that person"
That happens all the time. My Senator consistently voted in ways I don't like, so I'm voting for someone else next election and not contributing to his election campaign = stop giving support = cancel? Yet, entirely acceptable.
"withdrawing support for (canceling) public figures and companies after they have done or said something considered objectionable or offensive"
You'll note that "public figures and companies" has the built-in bias to the rich, powerful, and famous I mentioned - minimum-wage service employees cannot be canceled, according to this definition.
You'll also notice a long history of, say, the NRA withdrawing support from a politician after that politician support gun sale restrictions. And what happened to Kaepernick in the NFL is surely an example of cancelling, yes?
That is, both definitions are so broad that, when stripped of its specific anti-left bias, becomes no different than what John Stuart Mill says we should expect from liberty, and may even be our duty.