What do you see as the main problem with applying "That which can be destroyed by the truth should be" to liberalism?

Disclaimer: I haven't thought all of this through. As MTSW points out, "The idea that people are unequal in ways that matter is legitimately too horrifying to contemplate, so liberals deny the inequality, and conservatives deny that it matters." - I don't think I can think all of the consequences through myself, and I haven't seen anyone seriously discuss the potential outcomes of it.

But I think it may be useful to start with the fact that it matters how you select and present the "truths"; e.g. there is the whole Chinese Robber Fallacy, where you selectively present facts that makes a group look bad. Obviously this is not the sort of thing "that which can be destroyed by the truth should be" is meant to apply to; it's more meant to be for the cases of "that which can be destroyed by the whole truth should be", or something along those lines.

So bringing this around to group differences - one of the debates about group differences is what they tell you about individual traits. For instance, if women have much (d~1.2) worse mechanical ability than men, does this tell you things about any given woman's mechanical ability? On the one hand, the answer is clearly no/negligible; a group difference of 1.2 will (if I did my calculations correctly 😬) only reduce your range of uncertainty by 14%. You're still going to need to treat people as individuals and investigate their actual mechanical ability if you want to know how good they are. On the other hand, as MTSW points out:

Give people photographs of various women and men and ask them to judge how tall the people in the photos are, as Nelson et al. 1990 did, and people's guesses reflect both the photo-subjects' actual heights, but also (to a lesser degree) their sex. Unless you expect people to be perfect at assessing height from photographs (when they don't know how far away the cameraperson was standing, aren't "trigonometrically omniscient", &c.), this behavior is just correct: men really are taller than women on average, so P(true-height|apparent-height, sex) ≠ P(true-height|apparent-height) because of regression to the mean (and women and men regress to different means). But this all happens subconsciously: in the same study, when the authors tried height-matching the photographs (for every photo of a woman of a given height, there was another photo in the set of a man of the same height) and telling the participants about the height-matching and offering a cash reward to the best height-judge, more than half of the stereotyping effect remained. It would seem that people can't consciously readjust their learned priors in reaction to verbal instructions pertaining to an artificial context.

So men and women would regress to different means, which means that if your test of mechanical ability is imperfect, you would "rationally" discriminate against women. In fact it turns out that the usefulness of a stereotype for discrimination is highly nonlinearly related to the amount of information it provides/degree to which it reduces your uncertainty; as stereotypes that only reduce your range of uncertainty by marginal amounts are still highly useful. (When trying to select for someone who is high in some trait using a proxy, the degree to which you succeed in expectation will be proportional to the correlation r between the proxy and the trait - but the amount it reduces the uncertainty will be proportional to 1-sqrt(1-r^2), which is close to 0 for most of the range of r.)

(Sidenote - one point I've thought up a while ago, which seems underappreciated, is that how bad this is actually depends on some subtle causal relationships. In addition to there being a sex difference in mechanical ability, there is also a sex difference in mechanical interests. One theory goes that the sex difference in mechanical interests causes the sex difference in mechanical ability, because if you engage with mechanical stuff more, that gives you experience with it. Another theory goes that sex differences in mechanical abilities cause sex differences in mechanical interests, because it's not very fun to engage in some topic that you are bad at. These make somewhat different predictions because in the former case, interests screen off ability from sex, while in the latter case, ability screens off interests from sex; that implies that, in the former case, women and men who are equally interested in mechanical stuff regress to the same mean, while in the latter case, women regress to a lower mean than men even when equally interested. The former seems "better" in that the "women are worse at mechanical stuff" only applies to women who don't care about mechanical stuff anyway. Personally I suspect the former more accurately captures how it works, but I haven't seen it evaluated in detail.)

Anyway, what does this have to do with the Chinese Robber Fallacy? Well, if your test of mechanical ability wasn't imperfect - if you knew exactly how good everyone's mechanical ability was - then you would not be incentivized to rationally discriminate. So plausibly, equal treatment might be "destroyed by" knowledge of demographic truths, but restored by knowledge of individual truths. So truth about group differences may make group discrimination worse, while truth about individual differences may make group discrimination better.

But also, an unfortunate fact is that group differences are more legible and easier to measure. You can just select a bunch of people from each group, give them a relatively bad (but quick/cheap) test, and this will give you a fairly solid rank-ordering of the groups in the trait, because the noise cancels out. Then often group membership will be trivial to observe, as it is correlated with physical characteristics that are hard to hide, so you can apply this information about group differences as an ultra-cheap but highly inaccurate test of the trait value for individuals. Meanwhile if you wanted to know the trait value for individuals, you would have to test every single individual that you wanted to know the trait value for, and you would have to use a much more thorough but expensive test, etc..

So there's a Chinese Robber-style asymmetry, where the truths that increase group discrimination are inherently easier to obtain, spread, and apply than the truths that decrease group discrimination.

And then there's the issue of whether it's even desirable to know the individual-level truths. Truth and privacy inherently trade off against each other.

Surely people came to believe in liberalism for reasons that are in part empirical.

This is definitely a good point, but I don't know whether it solves it. As far as I know, the modern movements in support of gender and racial equality originate from all the way back when women and racial minorities were completely subjugated by white male authority. I feel fairly certain that one doesn't need group difference denial to see that this is wrong and immoral.

But this then seems to have birthed movements that have made group difference denial obligatory, which then seems to have increased the expectations for equality and the demands for policies to achieve it. If racial differences in intelligence don't exist, then not only should black people be allowed to do whatever white people are allowed to do, it's also indicative of hateful discrimination if black people achieve worse socioeconomic outcomes and therefore this discrimination must be stopped.

Presumably, acknowledging innate group differences isn't going to bring us all the way back to maximal oppression, and presumably it is going to cut down on some of the worst excesses of activism - but that still leaves an enormous range inbetween, of varying degrees of oppression, discimination, activism. Do I know where we would end up if we freely acknowledged innate group differences? I have to admit that I don't. Do I even know where we should end up? I might favor some sort of "treat people as individuals" liberalism, some go more egalitarian than me and suggest using the knowledge of innate group differences to achieve greater equality, and some go less egalitarian than me and want to cut down on immigration. And that's just the state currently, where there is much denial of innate group differences - what happens if the taboos start getting lifted?

(And what about backlash? If it's discovered that academics and activists have been lying about these topics for decades, what will the reaction to that be?)

(One issue is that the lack of agreement on a common political framework could cause conflict-heavy coordination failure, but I'm not sure if that's what you see as the main problem.)

Overall, I don't really have a main problem in mind. What I do have in mind is that I don't know what would happen. "The idea that people are unequal in ways that matter is legitimately too horrifying to contemplate, so liberals deny the inequality, and conservatives deny that it matters." - This is a topic that lacks investigation and discussion by smart people who acknowledge the inequality, care about the moral equality that has been achieved, and most importantly, care about the truth.

Feels like a sleight-of-hand to me that your post did not make clear.