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.
Big 5: http://www.yourmorals.org/bigfive_process.php
(You can see some of my results at http://www.gwern.net/Links#profile )
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 properly set. The lack of them will predict a small number of really smart people. Then there is a larger bunch of people who imitate that small number, follow them as authority, loyal to their causes and feel revulsion when their ideas are dragged in the mud, but still use the non-authoritarian, non-loyalist, non-purist language of their leaders. (This tribe would be called "liberal" in the American terminology. In many Easter European cultures too, in Western Europe just called "normal".) The vast majority of that tribe majority will have loyalist, authoritarian, and purist instincts, just not towards the common targets, and wrapped into a language that denies it. Loyalty to the group that identifies as disloyal individualists. Using Dawkins quotes as authoritarian discussion-stoppers, yet many of those quotes will contain funny, irreverent, anti-authoritarian bits. Conforming to non-conformism. Rebellion as a mass fashion item. These are not new ideas.
Note that you just made an argument for these being terrible bases for public and social policy in a diverse society.