"Guess it works both ways."
Sometimes it may well, but doubtful in your case, and certainly rarely.
Conservatives as a whole support the Constitution, which would include our 1st Amendment Rights, whereas Liberals oppose any and all contrary thought, especially that for which they have no rational defense for- which is pretty much everything they believe in.
Cancel culture is largely a liberal tool of censorship in our day, whereas, perhaps it was more on the other side back before the 50s. Ironically, it was the liberals of the 60s and 70s that stood up to that, and Conservatives, being the better people, backed off.
Now those same hippies of that era have grabbed hold of the very power they allegedly once hated so much, and use it as a bludgeon on any who dare to disagree with them.
I say allegedly, because they never possessed any true virtue in the first place. The things they insisted on having the freedom to express are generally an abomination to a civilized society, and they certainly have paid a steep price for their lewd and lascivious behaviors. But to those who are still alive today, they continue to push towards making this country into a totalitarian state.
I would have to see the original comment you made before I agree to your supposition.