Examples of "woke" efforts to stifle ideologically non-compliant literature are as varied as they are disturbing: removal of To Kill a Mockingbird from necessary readings (example), outraged social media enthusiasts trying to kill a writer's book before it even gets published (example), publishers mangling classics to purge them from any insensitivity (example), non-compliant writers subjected to vicious smear campaigns (example) and threats (example). Not to mention the unholy spectacle of intimidation and threats that surrounded the publication of that by all means insignificant book The American Dirt (example). And all these examples could be multiplied many times over, unfortunately.
Therefore, I don't think it is a false equivalence at all. I certainly agree that Florida's case is particularly egregious and taking novel, institutionalized proportions, but, taking a look at the big picture, we do seem to be witnessing a supra-ideological authoritarian turn, and it makes sense to look at it as a single, general phenomenon, which manifests itself differently in different social and political contexts, and which needs to be addressed on the level of the whole society rather than fruitlessly split over ideological lines.
I want to clarify these examples after looking them over, and explain why I think this a false equivalence overall.
TKAM: is not banned, simply removed from required readings in that particular school (I don't know what other readings they have that are required — I presume and hope that they are even more "anti-racist" than TKAM, or else something else is going on). The article states that profs who wish to assign it can.
A. Wen Zhao: she got backlash over an increasingly tired and problematic trope, the dangerous magical minority. Disproportionate to whatever was going on in the book, and proportionate (I guess) to the young crowd involved (this is YA). And then the book was published. And then the trilogy. She's still writing.
Dahl: not wokeness, but profit-seeking calculating that future people won't want to read slurs in childrens' books. Their calculation is of course highly scattershot/over-zealous (the Dahl examples are egregious and I'm not going to defend them; was anything lost by rejiggering Ten Little N*ggers in to Ten Little Indians/And Then There Were None?) and highly money-oriented (rejiggered texts can be copyrighted for longer than the originals which will fall into the public domain eventually). Wokenes is a fig-leaf here for the publishing house's bottom line.
CNA: is complaining about being (violently?) criticized on Twitter for (fairly mild?) insensitive comments. This (I guess?) can be chalked up to "wokism", but the comparison fails again. Also, it's all a bit
JKR: death threats are unacceptable. Also unacceptable is JKR lending support (which in magnitude dwarfs anything the LGBT+ community is capable of) to some of the worst transphobes on internet. I wish both would stop.
American Dirt: again, an author criticised for use of lazy tropes and inauthentic writing. I deplore that it focuses on her identity as such, but if the described experience rings false as well, the writing and writer have failed — and taken the place of perhaps better writing, under false pretences.
I'm sure you can find more examples, as you say, more or less attributable to what you would call "wokeness", which I recuse anyway as an umbrella term for many phenomena. But I see it as simply incorrect to both-sides this. The interplay of progress and reaction is more complicated than a "both sides have equal power and are doing equivalent things" position.