McCarthy was exactly the example of right-wing cancel culture I was going to use. It's extremely prominent; his explicit goal was to ruin the careers of people too left-wing for him, and it was successful for at least a time. Him being correct about there being lots of left-wingers around doesn't mean he isn't engaging in cancel culture. Most of the things left-wingers bring up to cancel people are entirely factual.
For the record, the rest of my examples here are going to be extremely Amerocentric, too. I'm sure if I spent an hour I could find an example of Tories doing something cancel-y, but I'm more familiar with American politics. So you could argue that Tories specifically haven't cancelled anyone, but I'm not so sure that's the case. Cancelling is not "left wingers taking down people who aren't as left wing as them", it's what happens when the whole of society decides to disapprove of someone due to their actions. Everybody has some kind of button to press, some ideology they will find distasteful enough as to refuse to associate with people who believe in it.
A good example today of right-wing cancel culture would be the far-right primarying moderate Republicans. If you are a Republican politician and you don't think Donald Trump should forcibly lead a military coup to retake America, your days in politics are limited. The party was lost to right-wing radicals decades ago, and they don't tolerate anyone outside their little black hole on the political compass. Hell, state GOP branches are already censuring the seven or so Republicans that voted to convict Trump. The only difference is that the cancelling here is limited to inter-party struggles rather than breaking out into the wider culture.
There's also that time right-wingers tricked Disney into firing James Gunn over vile things he tweeted decades ago. Cancel culture doesn't need to be ideologically consistent. We usually think of it as left-wingers getting angry about right-wingers and purging them; but it can also be right-wingers getting angry about left-wingers, and then making up a story to sick their lefty friends on them. All you need for cancel culture is someone who wants someone else socially gone, and another group of people willing to disassociate with certain ideologies.
Furthermore, to actually fight cancel culture, you either need to compromise on free speech and prohibit people from revealing someone's political ideology; or you need to compromise on freedom of association and make it illegal to disassociate from someone over their political ideology. I'm not sure either of those changes are actually beneficial.