Class-only leftists do not exist. This is a dank, embarrassing right-wing talking point that no IRL adult should entertain for even a moment. The accusation betrays a pathetic ignorance of both political history and Marxist thought. The very idea is facially absurd, and attributing it to one's critics is self-flattery of the dumbest sort.
Economism - the actual historical term for class-only politics - is mostly a relic of Enlightenment-era determinism. Their shared premise was that everything in the universe could be reduced to the basic interactions of the fundamental constituents of the material world. Saying that "everything is based on economics" here is just a shorthand for saying that everything is related through clockwork universe physics, which even governs things like the distribution of resources. Classical economists - capitalists as well as Marxists - quite often understood their work in precisely these terms. The guys who took this kind of thing seriously looked like this:
ICYMI, the common denominator here is that these pictures are old. These people have been dead forever. Lenin and Stalin purged most of them as "vulgar Marxists" - essentially their term for guys who held an incorrect and oversimplified version of Marxism. That's right: if you believed what liberals keep saying Marxists believe, the Soviets would straight-up kill you for being that dumb.
Notably, only one other political faction has ever equated leftism with economism: capitalists. That was a huge part of Max Weber's schtick, it was a big part of Reagan's schtick, and it's a go-to line of criticism on the American right even today:
History was then simply a question of economics to Marx and his friend Engels, and about who controlled the flow of goods and Capital in the world. This materialistic view of the world is thus what finally took over and mobilized the whole socialist movement until very recently. After coming up with this world view that basically everything is just money wearing different costumes, Marx went on to develop just how the whole system functioned so he could better topple it.It's easy to see why Capitalists would be so eager to associate Marxism with class-only politics: economism is as dead as it gets. What little intellectual currency it maintained in communist states utterly collapsed as it encountered the realities of governance - particularly faced with the rising tide of European fascism. For instance, in 1924, Carl Grünberg was arguing that "from the point of view of the materialist conception of history every single expression of the life of society is a reflection of the current form of economic life". But only six years latter, Torres notes,
Horkheimer replaced him as director [of the Frankfurt School]. He shared none of his predecessors' “scientific” optimism. In view of the threat that the rising tide of Nazism presented to an academic institution run by Jewish Marxists...the traditional Marxist economics of Grünberg, Grossman and Wittfogel were no longer able to explain the shape the world was beginning to take.Again: this was in nineteen-thirty. The last significant bastion of class-only politics among Marxists repudiated its own economism more than 85 years ago. Almost all of the people who lived to see the death of economism are dead themselves.
The Frankfurt School - which largely pioneered the more sophisticated investigations into relationships between sex, race, class, and so on which are today popularly explored through "intersectionalism" - represents just one of the diverse and prolific efforts among Marxists to understand power and oppression in its full multiplicity of expression. Generally, this enterprise can be described as an attempt to delimit what class analysis can tell us about the world - and what it can't. Liberal capitalists (and their conservative counterparts) who try to characterize Marxism as class-only politics are relying on an embarrassingly antiquated, cartoonish line of red-baiting, and revealing a frankly stunning ignorance of over a century of leftist thought.