Look, if YourMorals wanted to be culture-neutral, the first step would be purging terms like "liberal" and "conservative". (I know countries where "conservatives" are far more anti-capitalistic than "liberals" because their capitalism is largely controlled by foreign firms and they dislike that on a nationalism basis: better our government than foreigner's businesses.)
YourMorals is strongly US-centric, and the rest of the world like myself has to resort to rule-of-thumb heuristics to modify both input given and output received...
My input modifier heuristic is "how would those American movie actors I can identify with most answer". I expect others around the world doing something similar. For example, my list of questions is based on "what would Clint Eastwood and people around the world who easily identify with him reply".
I'm not saying it should be culture-neutral, I'm assuming that if "masculine thinking" is a real thing, then it's going to be culture-neutral, and we want to, as much as possible, separate "do you think in a masculine way" from "do you think in the way this culture prescribes for men". Otherwise, it'll just be a poll of gender identity with a lot of noise added.
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 )