But the moral foundations are naturalistic. If you find that there is a Volkischness axis that is well-supported by data and not explained by care/harm, fairness, loyalty, purity, etc., but otherwise has all the same characters observationally as other things that we classify as moral intuitions, then the conclusion is that Volkischness is in fact at least trainable as a moral foundation. Haidt doesn't claim that the five (or six) foundations are the entire foundation, just that they cover a lot. And he doesn't claim that they are independent of training and experience, just that they are widespread (especially the five original ones).

(Loyalty to a particular authoritarian leader is very nicely handled by the loyalty and authority axes already, so that is not a good example. Volkischness isn't really covered, however--it's really a particular view on how to structure the xenophobic aspect of tribalism.)

That Volkischness has a profound clash with care/harm and fairness doesn't disqualify it as a moral foundation. There are conflicts between moral intuitions all the time.

However, if we want to systematize the intuitions into a societal norm of morality, we probably would do well to reject Volkischness almost completely. Accepting it because it's there is just a straightforward application of the naturalistic fallacy.

And even if we ground morality in moral intuitions to prevent the infinite regress of oughts, we still would tend to observe that Volkischness is a really bad fit with almost all of the others (outside of a sparsely populated hunter-gatherer society--then it might be okay), so if any of them have to go, that would be it.

And you don't justify your apparent claim that you can wave a stick at anything and get as good of data as Haidt's students did in that paper, so while we should always hold our conclusions tentatively, I'm not sure that should even move the needle there.

(Also, of course, that there exist some people who advocate morally depraved actions on the basis of being Libertarian is no more reason that it isn't a moral intuition than is the observation that people will commit depraved actions on the basis of every other intuition.)

I do agree that we should question the framework, and I don't think we can entirely rule out that the centrist posturing, not just appropriate response to data that reveals deficits in the hypothesis, may have played a role. But to dismiss it on these grounds seems entirely unwarranted.