Really, Germanic professors who hated jazz invented multiculturalism? Not so much. And the French theorists came up with their ideas on their own without much influence from the Frankfurt School.
So far as I can tell, multiculturalism started in Canada and was picked up by the European Union. It had precursors in the reality of Central Europe and the idea of "transnational America" a century ago.
Sure, Foucault and other theorists inspired multiculturalism in the universities, but governments and bureaucrats got there first.
The Frankfort School was responsible for cultural Marxism - multiculturalism is an offshoot of that. The idea was to destroy western civilization out of guilt associated with colonialism and WWII; it wasn’t because German intellectuals either liked or disliked jazz. Multiculturalism is merely the device to ensure that the west is properly punished for its sins. It’s working quite well, too.