Lately I've been working on a fun piece about real class-only leftists from history - what they actually said, and so on. (Spoiler alert: they sound nothing like anyone alive today.) I'm doing this, of course, because critics continue to argue that the class-only leftists are still with us, and are in fact such a significant political faction that they warrant constant attention and censure. This isn't merely incorrect; it's silly, and my guess is that an encounter with actual class-only leftists from history will help demonstrate just how silly this actually is.
When I argue that actual class-only leftists don't exist, I'm really just taking at face value the common claim that they do. This is the fair way to have a conversation. In general I think it's a bad idea to read lots of subtext or secret intention into what your critics are saying - first because this often becomes a way to put words in their mouth, and second because it really is their responsibility to say what they mean. If critics want to claim that leftists only care about class, they should own it, and accept correction when it becomes obvious that this isn't at all the case in any meaningful sense.
That said, because I've been writing about this so much, and am evidently making little headway (even among people of good faith), I'd like to gently, tentatively, offer a modest theory about what is actually going on here.
When good-faith critics say that leftists only care about class, and don't care about the usual categories of identitarian oppression that are in play when we have this conversation (racism, sexism, and so on), I often get the impression that this is not what they actually mean. What they actually mean is that leftists care too much about the former, and not enough about the latter. Often, this critique will come when the leftist is simply defending or advocating a class-analysis. Or when the leftist pushes back against an analysis where she feels the role of class has been displaced or trivialized by other kinds of oppression. The critic will see this happen, and decide that the leftist has gone too far, or isn't balancing her priorities just right - and from here, he will argue that she only cares about class and only gives it a place in her analysis.
I suspect that there are two general reasons why this happens. The first is simply that intersectional analysis is extremely complicated and often unamenable to casual discussion and debate. Class oppression and other modes of oppression are so inextricably intertwined, and the ways they emerge and interact so extraordinarily subtle and situational, that it often takes a fairly Herculean effort to pin down exactly where points of disagreement are and what precisely one is getting wrong. For this reason, good-faith critics are just using "class-only leftism" as a kind of rhetorical shorthand for something like "disproportionately or incorrectly class-centered leftism", which is certainly efficient but not entirely fair.
The second reason, which I think is a bit less benign, is that simplifying a leftist's position to "you only care about class" makes for a really effective rhetorical cudgel. The stakes in these debates are real and often pretty high - even slight analytical differences can imply drastically different political and strategic positions - and so the temptation is to ramp up the rhetoric proportionally. An easy way to do this is to insist, unfairly, that what may just be an analytical error or disagreement amounts to the expression of latent bias or privilege or apathy. That may very well be the case, but it isn't necessarily the case, and it's fairly bad faith to just assume this.
Again, all of this is purely speculative and generalized, coming mostly from a place of intuition, and from bafflement that the "class only" charge is still one that anyone takes seriously. I wouldn't insist that this is necessarily what's going on in any particular dispute, but I suspect that something like this does happen in some of them. That, combined with the quite cynical and deliberate campaign by liberals and political operatives to willfully smear leftists as "class only" regardless of what they believe is creating a fairly toxic political environment for leftists who want to give class any place at all - so whatever the reasons for the persistence of this zombie critique, I think the left ought to take it fairly seriously.