I often prefer to talk philosophy with non-faculty people. Talking with tenured academics is too often difficult when their ears are so full of their own thoughts that they cannot listen, and their mouths so full of their own opinions they cannot speak clearly.

I have met and spoken with Honneth, and my PhD was done under the mentorship of someone who was mentored by Honneth. While I like him, I am also critical of his system, so much so that I wrote a whole book criticizing it, Rethinking Misrecognition and Struggles for Recognition: Critical Theory Beyond Honneth, https://amzn.to/3cLQgV8.

Your charge is correct that Honneth is guilty of prvileging one set of values over others. A number of critics have also leveled the same charge. Given your outline of a concept of real justice, I wonder what you think about Levinas' idea of ethics. I have a article on that ready to go. I was planning it for tomorrow, but I will go ahead and publish it today. He touches on the knowable commonality of experience, though differently than you seem to thinking. I agree with that general approach, but I have to wonder about the value of trying to make a distinction between "material existence" and beliefs, because any view anyone has of "material existence" is a belief. The issue, then, would not be beliefs but the knowable commonality of beliefs, which is a more fruitful area of consideration and necessary critical dialogue.