Ok, I'll admit I got a laugh out of this one.
It does highlight something pretty weird that's happened in the last 20 years; I'm about 20 years younger than Gen X, but even when I was growing up it definitely looked to my childhood eyes like it was mostly the right that wanted to cancel things they didn't like, whether the thing was 'violent video games', 'sex education', 'Pokemon cards' or 'teachers who explain to kids that gay people exist and are fine'.
I assume the dynamic has shifted because of generational turnover, after all section 28 (which prohibited the last of those) was only enacted in 1988 and repealed in 2003. According to the BBC coverage at the time (Link), the repeal became possible because "after the death last year of Tory former Lords Leader and prominent "family values" campaigner Baroness Young, peers' resistance to repeal crumbled."
If one outcome of the 'cancel culture' furore is that right-wing politicians stop doing things like that because they now have a committment to 'free speech and open debate', I might just consider this whole mess a win after all.
Unfortunately, people have short memories and it seems much more likely people of all political stripes will continue to try and sweep widespread views they don't like under the rug rather than interacting with them.