Concerning the conflict of Critical Activity as Critical Praxis vs Critical Thinking
Critical Theory vs Critical Thinking
The chief concern is: regardless of how one feels about one's access to objective truth and knowledge, yes, both sides can agree (because we have the subject/object split) that, regardless of whether you include the Marxian descriptions of Ideology and Conflict Theory and a hierarchized stratification of domination and oppression, both sides will agree in that subject object split. The difference is that, one has an understanding that there are methodologies which are the most accurate for being able to deduce what objective reality is.
The other is more focused on the transformation of reality to the point where that objectivity becomes accessible, and the subject and object are one.
One has it happen in this world, whereas the other one doesn't believe it can happen or that it can happen in a transcendental state beyond what can be understood through human consciousness and experience.
Now, what causes,a t least myself, to choose one over the other, is that even if we do agree in that disconnect from objectivity, Critical Thinking is superior because the only way that you can move towards it effectively is when you and your interlocutor are communicating in good faith.
There has to be that sentiment in the experience of each participant which allows it to take place, and if you have an understanding of false consciousness or a belief that those who don't share the perception are suffering from a false consciousness, then that sentiment will never ever manifest.
So you have to begin there - with that good faith - without the good faith it's just war and it's just who believes in truth or who believes that truth is worth it.