That's soft cancellation.

Hard cancellation is when you get others to gang up on them and go to HR to try to get them fired. Afterwards, you publicise whatever got them fired offline in the hopes that they become 'radioactive' to employers and so that they and their family fall on hard times.

I'm a little confused as to why people don't understand what "cancel" means in this context. Isn't it quite a popular topic nowadays? Is it possible that they're claiming ignorance, because they want to argue against the meaningfulness of the term?

I dearly wish that when people use the phrase “cancel culture,” they mean exactly what you say here. If they did, it would include trying to “cancel” people who sympathize with white nationalism.

But it would also mean people who belittle or demean others because of their gender. Or people who belittle, demean, and bully people with less experience.

One of PayPal’s founders once bragged that they declined to hire an engineer because they said they liked to “shoot hoops,” and PayPal was not a company where people liked to “shoot hoops.”

All of that would be “cancelling” people too, by your definition, and it’s all just as worthy of discussion.

Where I work, that sort of behavior is classified as "workplace bullying", and I think that's accurate. My concern with political discussions being common is that people will be expected to conform to whatever happens to be dominant in that workplace in order to remain on everyone's good side. I don't know if it would be possible to refrain from participating without being called out, because people will think you're hiding something.