WWI and the failed (communist) German revolution of 1918 put test to the communist theory that the workers of the world would unite to fight a class war on the rich instead of the state and ethnicity focused conflicts since time immemorial.
Marx's outline for Communism in Das Kapital was descriptive. It was him describing the way he thought the world would go, not coming up with a plan to make that thought happen. WWI showed the left, Marx's followers, that this glorious revolution wouldn't just happen, the social paradigm (culture) had to be shifted in such a way as to make the revolution possible. This is where the Frankfurt School comes in. Founded (like all communist projects) with daddy's money.
This theory about changing the culture is what the right today describes as "Cultural Marxism". It from this spring that our modern concept of critical theory welled.
They basically started the grievance based identity political discussion that has dominated US politics since the 60's.
Back to Weimar Germany.
The Frankfurt School's coffee house philosophy session couldn't defeat Nazi theory in Germany.
With Hitler's rise in '33 they left Germany for Geneva then decamped for Greener pastures at Columbia Uni. in NYC.
Their theories became popular with NYC's intelligentsia.
It is this movement that augured the lefts long march through the institutions in the USA. It started with Academia, then spread to media, politics etc etc etc.
This history and how clearly it draws the line from Marx' pen to the modern American left is why the term "cultural marxism" is such a thorn in the side to the left.
Any serious engagement with the history shows the intellectual history of the modern left not as some organic and fundamentally American theory space, arising from the unique characteristics of American life.
It came into being by fighting the right with billy clubs in the street of Germany after 1918.
Now the question becomes. Did America need this theory to overcome some of its hurdles in the 20th century.
This is where I depart from ideologically blinded rightwing folks and say yes, I do think the nation needed SOME of what they were selling.
Roosevelt had already started the New Deal by the time they got to Columbia in '33, and the country had recovered mostly by 1937. I don't think their philosophy played much role in American politics until you get to the red scare after WWII. Interestingly their presence in the country and their coming here in 1933 led to the kind of widespread elite adoption of communist thought that in turn led to the Red Scare.
America had to deal with its race issue to move forward as an ongoing political project. I'm not sure that happens as soon as it did or in the way it did without the salience critical theory. This goes as well for Womens issues around the same time. Generally we needed a shift in our thinking about race, and these theories provided the headspace for that to happen in America.
The problem that is now currently rearing its ugly head for the left, is the success and dominance of these ideas around critical theory. Yea we needed a little bit of that kind of thinking to get over our issues in the 20th century, but with the legalization of Gay marriage with Obergefell in the 21st, critical theory is now an answer in search of a problem.
The new problem it found was trans issues, which for a host of reasons has turned off the public to the cultural inclinations of the left.
The battles the modern left was born to deal with have been won. The problems in large part now stem from the dominance the left has had politically and culturally since FDR.
Just as FDR was and the left was needed to deal with the excesses of the era before it, our new political era requires an ideology tailored to mend the issues of the one before.
Which is why the political moment now feels so weird. Why our parties are now realigning (ie hispanics moving rightward, along with working class whites, and the rich moving leftward).
My personal issue with the left stems less from what their ideology is, though I do have massive problems with that, than their inability to see how dominant their cultural world view has been and is. My political life on the right has been an uphill slog. I suspect that eventually they too will know what that slog feels like.
TL: DR I hate the Frankfurt School of Philosophy, but I think any honest reckoning with it has to admit it was foundational to getting America to deal with civil rights issues that we had to in order to move forward as a going political concern.