It's a different story how knowledge is passed on or accepted by society.
We know that the proof of authority is the weakest and most unreliable type of evidence. But still the proof of authority dominates in practical everyday life. We believe things because our parents or teachers tell us, even if we had the possibility to check them ourselves from a scientific point of view. But parents and teachers are not the source of knowledge, they are only transmitters.
In the humanities ("Geisteswissenschaften", and similar disciplines) the situation is different. Knowledge is rather believable and not falsifiable, but only accepted on the authority of the person who uttered the sentence.
I'm curious if you have any evidence that this is a general trend. Your original comment is also wrong; the "Frankfurt School", one of your examples, does not ascribe particular authority to its members by virtue of being part of the "school"[1] - rather, it denotes a particular tradition, very similar to the way we use the term "school" in music. A school of thought[0] specifically denotes a commitment to a particular method or set of principles, not a commitment to certain personages. Although a school may take after one person, it's not because of the person but because of the content of their thought.
Besides, the Frankfurt School never claimed to be carrying out science. Other schools were, for instance, committed to certain ideas of science. These philosophical schools are ontologically prior to science.
[0] https://en.wikipedia.org/wiki/School_of_thought
[1] Habermas is a "member" of the Frankfurt School of thought, yet he is criticized by those inside and outside the school. This, at least, shows that a school of thought is not a dogmatic adherence to a person or their ideas.
From this perspective, there's nothing "wrong" with Newtonian physics as long as you understand the domain in which it is useful (essentially: larger than molecules, smaller than planets).
Newtonian physics, QM and relativity are all just stories we tell in our attempt to understand how the universe came to be as it is, and predict how it will change (with or without our own actions). They are all "wrong" in the sense that none of them are the way the universe actually is, but they are all "right" in the sense that they provide us with immense explanatory and predictive power when used in the appropriate domain(s).
Is Minkowski space wrong because it's not called space?
also even if there is no authority one still has to explain what we are doing here. Philosophy may not just be of philosopher. We are not Plato and Aristotle... and in fact I doubt many practitioner even listen to this speculation. but still they need to say something.
For example One may say we are trying to devise experiments to refute ... or is it really so? that is not we observe but to a certain extent per Kuhn I say not. And this popper Way and the anarchist way is just was to take about things.