"Not solely reliant on logic or common sense"... you say 'not solely', yet you speak about 'recognizing the total work of ideology' and seem to be making an assumption with the hope that it will bring you into a more critical approach by some kind of counter-reaction. Very weird reasoning. One cannot claim that everything is culturally bound, nor that common sense (or wisdom) would always be a mere cultural/social construct. Sometimes they are, other times not so. A rational approach is also about recognizing one's own limits and realizing tendencies of taking something as the final (common sense) base, the absolute truth.
That's why I said that this seems to require people capable of sensing when they start to take as definitive things that are not so, when it is the moment to halt an analysis, or to continue it, or to declare it undecided. I rather tend to say it's a matter of teaching people to think critically, purely and simply, a bit like French school did before the advent of libertarianism in education. Free at last! Free at last! Thank God Almighty, we are free at last! (Martin Luther King)
My approach is to question everything - the critical approach that you seem to think the left are utterly incapable of. Who can really truly say where the line should be drawn on what is culturally bound or not? If you took some of things you consider to be absolute common sense and tried to apply that to a tribe in Africa or the Amazon, would it still stand? Would it still stand if something that is common sense and in no way culturally bound in your opinion, in France was compared to another European country?
You have made a number of assumptions about many different things here, whilst inconsistently saying that these very things should be questioned. Ad astra per aspera
But as I said above, while doubt, keeping an open mind, questioning and self-questioning, are fundamental, this shouldn't stop one from being pragmatic about things, and avoid getting closed in a vicious circle of relativism. If we quit the philosophical scene and leave aside ideologies, we'll likely notice there actually are quite a lot of things we know already, but refuse to see, admit, or whose importance we diminish because it doesn't fit with our previous positions or preferred ideology. The only way to show there's no artificial bias, is sound, honest argumenting.
I gave several examples, that I called obvious:
The only way to show my good faith and my only concern: finding the truth, was to present the two facets and frame it as a question. Can you really not see how precipitated, ill-thought and ideological these conclusions are?
Of course, you can always turn my reasoning at me and say that by claiming common sense, I would decide what is true and what is not, I would bring forth my certitudes. This will always be the risk for rational pragmatists: "how dare you say things are so, impose your own truth, claiming logic and pragmatism? it's just a rhetorical method to exclude others' truths!"
False issues. Theoretical. Ideological. We actually know a lot of stuff as true already; relative stuff is much less than we like to admit. Nuancing is not the same thing as relativism. Seeing both sides of a problem, for instance, the employee's and the manager's, the man's and the woman's, the immigrant's and the local's, is an indispensable tool in finding solutions, and a proof of fundamental good faith. Free at last! Free at last! Thank God Almighty, we are free at last! (Martin Luther King)