The idea of 'cultural marxism' is the big fad on the American right these days. I made the mistake of trying to figure out if there's anything to it, or whether it's just another bizarre conspiracy theory.
Since Tablet magazine normally publishes coherent essays, I'm taking this essay as one of the better arguments that there is something meaningful to the term (regardless of whether it is used coherently in typical online discourse).
Having read half the essay, I'm not on my way to being convinced.
The argument seems to have three steps:
1. post-Marx marxists decided that culture mattered. That it was shaped by the ruling class to support their political agenda.
2. The marxists then determined that they would have to challenge the cultural hegemony of the ruling class.
3. Somehow this brings us to the modern American left (with some sort of intolerance for ideas that support oppressive institutions).
The first point is trivial. It seems obvious to me, but maybe that's because I'm influenced by Marxists. But I'm pretty sure this idea can be found as far back as the US slavery abolitionist movement (where F. Douglas described how Christianity was shaped by slavers to support the institution of slavery) and the French revolution (again, where the church was seen as an extension of the state). It probably goes back much farther. Another critic noted Hobbes. Maybe the Reformation too. I'd expect you could even find this attitude in the ancient world...every revolutionary will find that traditional culture was an extension of the traditional ruling class. And the mechanism is easy enough to see - the ruling class has the resources to create cultural artifacts and to promote and deliver these artifacts to an audience. There are plenty of examples from history of the elite judging culture by whether it will put the wrong ideas into the heads of the lower classes...and making efforts to purge dangerous ideas from the culture.
The second point seems trivial too. Of course the Marxists would recognize this. Here is the watered down conspiracy theory. They were pretty open about their intent to challenge the status quo of culture. I'm sure they did it with some amount of success. But it's a huge leap to suggest that Marxism is the only (or primary) source of criticism of traditional American culture.