How easy is it to test for things without being culture-specific and tradition-specific?
Haidt's authority foundation, for example: how would you test for that? You could ask people to identify authorities in their lives, but maybe they don't make the connection between the word and the concept -- how many people who believe the NYT, the "scientific consensus", etc. on faith would recognize that they're doing so? You can't test that by asking about the military; the people who think the NYT on authority are probably less likely than the people who don't to think that the military is a legitimate authority whose commands can be trusted.
And what about the purity foundation? Haidt has written a few times about liberal purity, but it hasn't been incorporated into the test yet. It's not hard to see that it exists: concerns about the purity of food, disgust-evoking metaphors for illiberal positions and the people who hold them, and so on. Inorganic food is full of toxins and nationalism is a revolting disease. But how would you test for liberal and conservative purity at the same time? You'd have to go meta enough to capture both (as well as the concepts of purity that exist in every other cultures) in such a way that the people taking the test would not only know what you're talking about but also make the connection between the concepts you're asking about and the things they're doing.
Given the memetic success of Haidt's test (a college professor I had referenced it in a lecture a few times, and said he'd heard about it from NPR), it doesn't appear obviously wrong to a lot of people. This could be because they legitimately haven't seen evidence of liberal concern for the other foundations (which would imply social distance from at least certain strands of what Haidt calls liberalism), but it could also be because they don't make the connections between that evidence and the concepts.
It's not hard to miss connections. I've ordered fast food innumerable times in my life, so I've heard phrases along the lines of "the meal, or just the sandwich?" after ordering a burger. But I still didn't think burgers counted as sandwiches until someone pointed it out a year or so ago. (It's probably relevant that I'd never seen a sandwich on a roll [circular, bunlike] until this year -- burgers are nowhere near my image of the prototypical sandwich.) And this is a case where there's no major political movement with an interest in making people miss those connections! Part of the memetic success of the five-foundations theory is probably that Haidt provided academic evidence for what liberals already liked to think about themselves.
It may be possible to find a way to test for these things culture-neutrally, but it's much harder a problem than you think. The question of masculinity would probably also need separate tests tailored to separate cultures -- or you could have a test measuring the extent to which the test-taker follows some number of different forms of masculinity. Some cultures are honor cultures, and some cultures aren't, but in honor cultures, honor tends to be in the male domain.
More general: fairness and caring are pretty universal, but purity, loyalty and authority are not only culture-specific, also political tribe-specific, and there are huge mistake potentials here, what is authority for one is a proper expert for another, what is purity for one is understandable revulsion over an immoral act for the other, what one sees as disloyalty can be loyalty to a non-standard group and so on. In fact, my prior would be that loyaly, authority and purity will not predict major political tribes at all when the questions are truly proper...
In 2011, InquilineKea posted a Discussion topic on YourMorals.org, a psychology research website which provides scores of psychology scales/inventories/surveys/tests to the general public to gather large samples. Niftily, YourMorals lets users sign up for particular groups, and then when you take tests, you can see your own results alongside group averages of liberals/conservatives/libertarians & $GROUP. A lot of time has passed and I think most LWers don't know about it, so I'm reposting so people can use it.
The regular research has had interesting results like showing a distinct pattern of cognitive traits and values associated with libertarian politics, but there's no reason one can't use it for investigating LWers in more detail; for example, going through the results, "we can see that many of us consider purity/respect to be far less morally significant than most", and we collectively seem to have Conscientiousness issues. (I also drew on it recently for a gay marriage comment.) If there were more data, it might be interesting to look at the results and see where LWers diverge the most from libertarians (the mainstream group we seem most psychologically similar to), but unfortunately for a lot of the tests, there's too little to bother with (LW n<10). Maybe more people could take it.
You can sign up using http://www.yourmorals.org/setgraphgroup.php?grp=623d5410f705f6a1f92c83565a3cfffc
All quizzes: http://www.yourmorals.org/all_morality_values_quizzes.php
Big 5: http://www.yourmorals.org/bigfive_process.php
(You can see some of my results at http://www.gwern.net/Links#profile )