Stv, I concede that you are right that both sides of the ideological spectrum are guilty of these vindictive power plays. I'm wouldn't categorize many of your instances as cancel culture, but I think it's probably a difference without a distinction.
The difference I do notice is that in this day and age, right wing consumers and employees lack the cultural influence and power to move the needle on cancelling their opponents. The vindictive power plays from those on the right seem to be mostly coming from individuals with far more resources than the average twitter user. I see left wing twitter trolls wielding far more cancellation power than their right wing counterparts, which is pretty fascinating. Maybe there's more to it than my earlier theory about urban areas (which overwhelmingly tend to be more progressive) and how their growing economic and cultural power lead to this, but I'd have to think more about it.
The nature of conservatism is being slow to adopt new things such as Twitter and new ideas such as cultural influence. This is perfectly natural behaviour.
Conservatives have traditionally used religion and other long standing power structures to exert cultural influence over things . . . but it's flat out wrong to say that they don't use or are slow to adopt social media. Facebook, twitter, instagram, whatsapp, tumblr, pinterest, viber . . . all have large numbers of conservative content producers and consumers. Conservative traditional media (tv/radio) is now so far to the right that they claim generally unbiased news is left wing.
I suspect that the relative lack of success they've been having recently is more due to the fact that the modern (socially) conservative message isn't very logically consistent.
Save the babies from abortion - every life is precious!/Fuck the babies on food stamps - life isn't worth dollars!
Let the free market control everything! / Fuck immigrants, they work for less money!
Religion is super important, devotion and church going is how you live a good life and should inform most of your decisions / Fuck Muslims!
We need to do something about crime! / Fuck background checks for weapons! Fuck proven prison programs that reduce recidivism!
FREEEDUMB! / We have to suppress the vote at every chance, especially those nasty black people!)
There is no such thing as racism! / We love our openly racist president!
There's a level of doublethink required to go along with these messages that just doesn't seem to be winning over the majority of people these days.