There was a great line in last Sunday's Curb Your Enthusiasm where Larry David (half) jokes about free speech, saying something like "I don't know about free speech. Well,
I should have it. The constitution should have said free speech for Larry David, everyone else, check with him first."
Larry is effectively holding up a mirror to the type of people you describe, and yeah what you say is true about people who complain about cancel culture, too. I try to engage anyone worried about losing a job due to something like that. I'll ask, why don't you organize with your co-workers and collectively bargain for labor protections, or consider voting in politicians who are for stronger labor laws, and all of a sudden they remember that their corporatist leanings are stronger than any feelings they may have about the "cancel culture" boogeyman.
It's plain to see that too much of the discourse about free speech or cancel culture doesn't come from a place of good faith...