In this podcast from the publisher of Zero Books, it's claimed that The Frankfurt School was brought to the US by the CIA to combat Stalinism/Stalin (not sure which, specifically); additionally, it also mentions that organizations and/or activists and/or artists on the Left were funded by the CIA for the same purpose.
Do these claims hold any water in mainstream historical documentation and analysis?
There really is not much truth to that particular charge as it relies upon conflating a number of separate actions into something more sinister. Many of the individuals that comprised the Frankfurt School did end up inside the US during the Second World War as refugees from the Third Reich. These emigres worked as consultants to the Office of Strategic Services, the predecessor of the CIA, to understand and defeat the Third Reich. Such wartime connections continued in the immediate aftermath of the Second World War, but the OSS/CIA found them of little utility to US interests. For example, the de-Nazification guidelines that Marcuse, Kirchheimer, and Neumann wrote were largely ignored by the occupation authorities.
One of the well springs of the rumor that the Frankfurt School were funded by the CIA came from the latter organization's funding of various magazines and journals to promote the non-Communist Left in Europe. The American Congress for Freedom and Culture, a foundation largely funded by the CIA, helped establish many of these new media outlets. Der Monat was one such publication and a number of Frankfurt School writers contributed articles to it. Similarly, several Frankfurt School-affiliated individuals would take up positions in various transatlantic academic institutes, many of whom were staffed by the former OSS colleagues and of course, there was US government funding for these initiatives. This created an impression that the CIA had suborned these individuals, but it relies on a very skewed understanding of how public intellectuals work and function. Der Monat provided a public venue for intellectuals in a time of great material dearth, and they naturally took it. Governmental funding for various think tanks is relatively normal in academia, as is the necessity of social networking to gain access to these institutions. So to speak of the CIA or American government as funding the Left is somewhat disingenuous as it was often done via fronts, as in the case of Der Monat, and really did not depart from established academic practices for funding international scholarship that are integrally connected to public diplomacy.
Sources
Berghahn, Volker R. America and the Intellectual Cold Wars in Europe: Shepard Stone between Philanthropy, Academy, and Diplomacy. Princeton, N.J.: Princeton University Press, 2001.
Parkes, K. Stuart. Writers and Politics in Germany, 1945-2008. Rochester, N.Y.: Camden House, 2009.
Wiggershaus, Rolf. The Frankfurt School: Its History, Theories, and Political Significance. Cambridge, Mass: MIT Press, 1994.