The problem is that right wingers seem to feel that they're part of the conversation. Nobody involved in what they call "cancel culture" cares what right wingers think. They already know what right wingers think. In the US, the right wing exists to oppose everything left wingers want -- even if it's something they used to like. We already know that. It's predictable and obvious.
This is a conversation that the left wing has within itself. Unlike the American right wing, where an irreligious, adulterous, multiply-bankrupt draft dodger can become the universally-beloved darling of the "law and order party" because they are exciting and therefore win elections, the left wing is asking itself hard questions. People aren't always good, even the ones you like, and you need to decide what you're going to do about that.
There's no way to discuss that without elevating it. There's nothing wrong with people knowing that JK Rowling is a transphobe, and that some people are going to be angry enough about it to want to be shut of her. They see transphobia as a threat to themselves, and it won't go away by pretending it doesn't exist. That means airing it.
As I said, nobody really cares what right-wingers make of that. It's safe enough to treat all right wingers as already transphobic: they will, reliably, vote for transphobic candidates, and mock those who want to deal with trans issues because they themselves don't have to care about it. The discussion doesn't involve them, and if they happen to hear about it and invent new epithets to call left wingers, that's just Tuesday.
I'll close by saying, even though it's really not the done thing, that I do find it amusing that I'm about to be downvoted into oblivion by people complaining about "cancel culture". That, too, is OK. I've said what needed to be said, and it's part of a difficult conversation that will be full of false starts and failures. Even among people who didn't reach for the downvote button six words in, there are actual, genuine disagreements that need to be worked out. If it happens here, fine. If not, it will continue to happen.