There's a lot of assumptions in what you're writing, which, despite you insisting to be "critical" of, are sustained by liberal ideology. You just assume that what you mean by "reason" is objective and equally accessible to all. As if it was just a matter of tuning into a television station, and some are just too emotional to do so. But I question these universalist assumptions. Indeed, in these situations, I'm inclined to ask (in the words of Alasdair MacIntyre), which rationality? And for that matter: whose?
Could it be that, what is rational and true for, say, an employee might be very different than what is true and good for their obscenely wealthy employer? For one it's just good business sense - i.e. rational and true! - that squeezing every bit of labour out of the other, regardless of the physical or mental costs, is what one should do. And a political party vying for power which seeks to upset this arrangement - by increasing worker representation or health and safety rules - is wrong, i.e. works against what's true (at least as far as market logic goes). But for the other, the employee, that party might be "speaking truth to power".
This is why critical theorists are interested in *power*, something which isn't always simple to quantify (like the vast majority of human measures). And it is why I'm so insistent that liberal ideology is leading people astray. In liberal discourse, we're all equal and free, and it's easy to believe so if you're cloistered. But in reality we're in a mess, frankly.
Also, I really wouldn't be so quick to dismiss what you call "lived experiences". What is your alternative? Line graphs? Pie charts? Don't you think that such disembodied things are just as open to manipulation? As Christopher Lasch said, in the hands of propagandistic power centres, numbers of this sort are often "accurate but meaningless"; socially useless. Steven Pinker is a case study in that.
And plus, Marxists claim to be just as critical of their tradition - and indeed if you get into their readings, you'll quickly realise that they're much better at self-criticism than most philosophical liberals. For one, Western Marxists had no issue describing the Soviet Union as "really existing socialism". In other words, they weren't screeching, "that's not real Marxism!" as figures like Jordan Peterson would have us believe. The most loud liberals (Top Lobster among them), on the other hand, can't even bring themselves to admit that Western nations are liberal. They rather pretend nefarious academics have somehow subverted the entire socioeconomic foundations of these countries.
Most things these champions of liberalism claim to despise - racialized divisions, class strife, the debasing of intellectual culture - are products of the industrial, liberal, capitalist structures which increasingly dominate the planet. Now, as far as I can see, that's a *truth* too distasteful for many to swallow.