I’m not convinced it’s different from “cancel culture as it is”. One common theme I’ve seen — including in this thread! — is people creating a dichotomy between “free speech” and “feelings”. Usually that means they want to say something controversial, but their own feelings get hurt when they receive pushback, so they try to reframe the debate in such a way that they’re the aggrieved party.
The “insult my boss” is a good thought experiment because it reveals that motivation. Is it really about “free speech” vs. “feelings”, or is there something else going on?
The boss situation is a lousy experiment because its result tells us nothing about what the result should be in the situation we're discussing. (For one, my boss isn't going to fire me by threatening the business if I call him a fatty.)
For example, it's relatively easy to figure out who the person is behind this account. The mob could decide that I've "done wrong" and go after my income. That's no where near me screaming at my boss that he's a Nazi or a fatty.
FWIW, "free speech" might not be the right hook - toleration might be more accurate. After all, many of the cancelers justify their actions as "we tolerate everything except intolerance."
The answer to "must my boss tolerate me calling him fatty?" is probably different from "should my fellow employees lose their income because A says that I called B 'fatty'?"
And then there's the fact that the cancellers go after everyone who might employ me. My fat boss doesn't have that kind of reach.