Your reply makes an excellent case-study in the epistemological bankruptcy of "critical" thought!

You just assume that what you mean by "reason" is objective and equally accessible to all.

Firstly, no, I don't. Reasoning is widely studied in children, animals, and adults (crows are awesome: https://www.scientificamerican.com/article/crows-understand-analogies/). We know quite well how accessible it is to different people (the distribution of reasoning skills, that is), and furthermore, "reason" is used specifically by me (and by most people) to mean that logically valid manipulation of premises that retains objective accuracy through the manipulation to reach new valid conclusions. "Reason" is different from "being reasonable", which is subjective.

Let's now consider the converse: "reason" is subjective and we don't know to whom it is accessible. Maybe it's not to me, maybe not to you. Well, I have news for you: I have my own truth! My truth is that there is reason! My truth is that if I hiss like a cat, my truths cannot be challenged! Hisssss!!! (Having embraced the converse opinion, you now have to admit that we are at an impass, with your view no better than mine--and you further must admit that no onlookers should believe you have a more realistic point of view than I do. And then you have to realize that even that reasoning is, oops! Reasoning! So actually you were just hissing the whole time. It didn't necessarily mean anything. But, oops! Reasoning again?! Can't even say that! Or...wait...that I can't say it is reasoning too, so I CAN say it! Whatever! Hisssss!!!)

I'm inclined to ask (in the words of Alasdair MacIntyre), which rationality? And for that matter: whose?

The objective one, the one that everyone can find from the Greeks to the Chinese to the scholars of the Islamic golden age to the Enlightenment philosophers.

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?

You smuggled "good for" into there. In most cases, that's subjective. Nice try.

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.

No, it's true for both of them given the right premises. Given the wrong premises it's either false, or it is not determined either way (i.e. there are models in which either could be the case).

Rationality is a tool, not an outcome. The employee can agree that in order to maximize business profits, at least in the near term, the employer should seek to pay employees as little as possible. The employer can likewise agree that to have a comfortable (or extravagant!) life, the employee, at least in the near term, should seek to be paid as much as possible. Both can recognize the other as being rational in this regard, and thereby identify the source of the disagreement: the premise that maximizing business profits is the aim on the one hand, and the premise that having a comfortable/extravagant life is the aim on the other. And they can reason still further, perhaps, and discover that they both actually have the same personal aim because the employer's reason to maximize business profits is to have a comfortable/extravagant life themselves. But there is an intrinsic conflict here, and there's no guarantee that we can use reason to solve it, only to bring it into relief. At some point we may have to make a subjective decision, but it's VERY far removed from the place you indicated.

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).

A liberal doesn't say power is unimportant. There's a perfectly reasonable liberal justification for unions, for instance. Critical theorists in contrast have a worrying tendency to elevate opinions to the level of truth, thereby rendering the concept of truth incoherent and useless, and having lost that, are left casting everything in terms of power. (Which is also incoherent, since my truth about power isn't necessarily your truth about power.)

Also, I really wouldn't be so quick to dismiss what you call "lived experiences".

I don't completely dismiss them, but critical theorists seem to display little to no explicit awareness of their massive flaws. (E.g. they are incompletely conveyed, they can be mutually contradictory, their expression can be untruthful, the details can be misremembered, and so on.) I asked you for an example of any critical theorist writings on how to tame these problems and I didn't hear anything from you. Doesn't necessarily mean it doesn't exist, but it's not the most encouraging sign.

What is your alternative? Line graphs? Pie charts?

Yes, please! With open data, clearly described methods, and error bars! Absolutely, whenever it's possible!

Don't you think that such disembodied things are just as open to manipulation?

No, not remotely. The point is not to show a bunch of squiggly lines. The point is that they convey something about objective reality which has been measured to a degree of precision that we have some handle on. And we can check how sensible it is to measure that thing (wage disparities, maybe), and thereby either come to a conclusion or get some ideas of what additional information we need in order to come to a conclusion. Of course you need an educated population to be able to do this...and guess what, liberals deeply value education!

As Christopher Lasch said, in the hands of propagandistic power centres, numbers of this sort are often "accurate but meaningless"; socially useless.

Sure, but they are transparently so. This allows us to catch them, throw them out, and get better numbers next time. Can you do that with "lived experience"?

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.

Well, sure, I guess I'll fold critical theorists broadly into Marxist thought. I haven't read much non-critical-theory Marxist work save Marx himself (the bits I have haven't been encouraging). But my sense has been that the pragmatic failure of their ideas has just been so abject and comprehensive that they have had no choice but to face it. In Traditional and Critical Theory, Horkheimer makes a bunch of predictions about things you can't do in a liberal framework, and it's astounding how comprehensively wrong he was--almost everything he mentions has had notable successes in liberal frameworks. And more garden-variety Marxism has an even worse track record.

I do agree that there have been tendencies for critical theory to approach arguing itself out of existience, which would be quite a triumph of self-reflection.

And I agree that liberals have been insufficiently self-critical, allowing considerable capture by corporate or populist or other inherently illiberal interests. There is, I think, some point in asking whether human nature is compatible with classical liberalism especially in regards to whether the necessary self-criticism for a successful liberal project is in fact achievable. There is also a discussion to be had about whether the liberal framework is well-suited to meet deeper objectives like human flourishing. The answer might well be "no", given the considerable failures of largely liberal democracies (though one must measure those against the considerable successes, too, and keep in mind that most every other scheme has had dramatically greater failures). I'm not quite ready to give up on it yet, but I admit that it's unclear whether it can withstand its challenges.

Could it be that under the weight of its own self-scrutiny, carefully applied in contexts where it's possible, the liberal viewpoint would be revealed to be inherently unable to deal adequately with human nature? Sure. And then I would accept that whatever comes next should perhaps not be called "liberalism" but rather something else. (For instance, "communism with Chinese characteristics" is not liberalism; it also isn't Marxism.)

But critical theory's successes (and there have been some, including in critical race theory) have as far as I can tell been in spite of rather than because of its epistemological perspective. There is no contradiction between taking a systems-level approach and using a traditional liberal outlook, for instance. Likewise, there is no contradiction between having a liberal outlook and taking a skeptical view of the current condition and society. We can preserve any of the useful perspectives that critical theory has suggested while still jettisoning explicitly the destructive epistemological baggage that it formally picked up along the way and mostly didn't bother using because it was too busy criticizing systems from within themselves to realize that its own extensions to the system didn't even make that a coherent concept.

In other words, and irrefutably from my lived experience, hissss!