I think you make a number of good points (and I encourage readers to revisit those and not assume that because I take issue with some points that I take issue with everything).
However, I think that although you've identified real problems, in some cases I think your explanation for the cause is highly improbable.
The biggest culprit that you place on the wrong side of the ledger is, I think, critical theory; with intersectionality a close second.
Intersectionality is, in a sense, true. It is not remotely new with Crenshaw, however. Statisticians have been understanding "intersectionality" forever, except in a more sophisticated way from the start (c.f. "covariates", though when Fisher introduced it in ~1949 it wasn't a new concept). The problem with intersectionality as a fuzzy label to apply to social situations, however, is that it emphasizes some of our worst anti-social traits: xenophobia / tribalism. Practically every great social movement has been powerfully motivated by unifiers, people who stress what is universally good, people who stress common humanity, and so on. We need constant reminders that we're all human or we quickly decide that since we wear our hair long and you wear your hair short, you are evil and deserve to be annihilated. Rationally, individually, our behavior makes no sense...but evolutionarily it sorta kinda does...and anyway, empirically we see it all the time. Intersectionality emphasizes that you should be on your side with those most like you; it fragments rather than unifies. As an analytical technique, it's useful but poor, because it only deals with categorical variables, not continuous ones, and again, it's not remotely novel. What is novel is that people were ignoring it, and Crenshaw among others helped get people to pay attention (and that is a big contribution, because there have been many instances where people have ignored that certain covariates that shouldn't be are predictive of bad outcomes (in the statistical phrasing)). So--telling us to use the tools we already knew how to use, to check to make sure that our tribal tendencies aren't sneaking through and causing cruelty in specific cases: absolutely, great idea, fantastic! Intersectionality as a conceptual framework upon which to organize a healthy happy society? Seems very, very difficult--and the evidence so far seems that our attempts are going badly. (You give an example yourself!)
Critical theory is worse, but less obviously so. The biggest problem is that critical theory seeks to do better than a dispassionate analysis by pandering to some of our most insidious cognitive biases. In brief, the problem with critical theory is that it has a terrible model for practical epistemology, leading to adherents being moderately divorced from reality and unable to convince anyone of their views because, well, they're not based on anything solid. The two portions of critical theory (CRT especially, but you can find echos of this in Horkheimer even) that are most worrying are (1) scholar as activist, which pretty much guarantees a very very strong confirmation bias in everything you do--ironically undermining the very critique that was supposed to be so enlightening in the first place, and (2) elevation of anecdote (as part of "narrative") beyond any reasonable place for understanding reality, leaving individuals isolated in their own truths (i.e. subjective outlook, often in contradiction to an actual reality)--this triggers all sorts of cognitive biases including improper generalization and more confirmation bias. Far from being a way to reveal and combat the dogmas of everyday thought, critical theory gives its practitioners the tools to self-righteously bamboozle themselves, and only intense discipline (and deep training in actual useful epistemology, like the practice of law or science) can partially save it. The dichotomy is particulary apparent when you read Bell or other founders of CRT: you can see them blatantly and repeatedly ignoring the tools that critical theory empowers them to use, in favor of a highly persuasive fact- and reason-based analysis as emphasized by the traditions of rational thought as developed since the Enlightenment. (Bell, Crenshaw, and others make fantastic and very persuasive and well-evidenced points in many of their writings...but...it isn't critical theory that is telling them they have to do this! They're allowed, but they're not required unlike with a standard "Enlightenment rationality" approach.) However, when you see people trying to use the techniques of critical theory divorced from this key anchor to intellectual soundness, the results are poor. Furthermore, in order to maintain a consistent outlook despite having rubbish for an intellectual foundation, practitioners are forced to lean on other techniques like virtue policing.
In particular, the canceling of Adichie is a pefect example of the problems caused by intersectionality and critical theory. The narrative of the trans person can be cast as one of oppression; critical theory insists that you be an activist, so you must resist this oppression; the individual account of a trans person who feels slighted by use of a word must be believed (you cannot imagine what pain your words cause them); you can't prove any of this so you must virtue police stringently to prevent harm; and because they are in their own intersectional group and are under threat from people who "want them dead", you needn't think about overall balance, intent, realistic impact, or any other mitigating factor. Therefore, an entirely reasonable, highly expected outcome of intersectionality and critical theory is that Adichie gets cancelled for insufficiently carefully self-policed language.
This is awful.
But the approaches you advocate for yield exactly this. Like many types of activism, feminism has fallen for many of the poor ideas. (They feel so virtuous! And easy, compared to fastidious studies and difficult deliberation of tradeoffs.)
In contrast, it is the rational, empirical, humanizing approach--the ideal though not the reality of classical liberalism--that specifically avoids this.
As a whisper in our ear when we're about to make a mistake: "Do we actually know what we think we do? If so, how do you explain this anecdote? Did we account for differences between groups? Have we turned off our moral compass and are we coldly accepting injustice?", critical theory and intersectionality add value. Anything beyond that, though, and they invite a cascade of increasingly bad errors.