"Frankfurt School Critical Theory" went through several generations with different commitments and each of those generations was quite politically and theoretically diverse.

The only true statements that hold for all writers at all times are largely uninteresting.

What can be said with confidence is that Frankfurt School theorists were not "counter-enlightenment".

Adorno and Horkheimer were explicitly trying to explain why the ideal of the enlightenment - greater rationality in social and political affairs and a fuller realization of individual moral autonomy - had not been achieved in their time. They saw themselves, rightly, as more faithful heirs to the tradition in their attempt to "rescue" it than those who insisted it did not require rescue. You may disagree - many within the tradition of critical theory have - but I don't think readings of their texts which see them as "counter-enlightement" can be sustained.

"I wondered to which extent Habermas with the Frankfurter Schule and Critical Theory could be held partially responsible for postmodernism's march through the institutions, identity politics, and indirectly for Trump's two election victories."

With all due respect, this sentence betrays a complete unfamiliarity with "postmodernism", "the long march through the institutions", and "identity politics". It wildly anachronistic to conflate these. It makes about as much sense as saying that Mitterand was an Avignon pope.