I don’t understand the inclusion of cancellation in this argument. How is cancellation different from boycotting, a right long upheld by the Supreme Court with direct legal ties to freedom of speech?
Cancellation is different in that it attempts to "boycott" an individual for holding non-majority views. If you can no longer get a job because you are vocally pro-choice for example, that's a problem. The state should protect someone's right to express their beliefs. This means that you will have pro-life / pro-choice people at the same company, and that needs to be ok. If it's not, it has a chilling effect on freedom of speech.
"Boycotting", "cancelling", both seem to be democracy in action. And non-majority views is too ambiguous a definition. This would put vegans on the same side of the scale as extreme race purists.
But that's just it. The law needs to be able to distinguish and provide proper protections. I do not think the public at large should be making that distinction because it turns on mob rule.