(And I'm pretty sure that many common LW positions would be considered idiocy in the larger world.)

Having come from there, the general perception is that LW-ers and our positions are not idiots, but instead the kind of deluded crackpot nonsense smart people make up to believe in. Of course, that's largely for the more abstruse stuff, as people in the outside world will either grudgingly admit the uses of Bayesian reasoning and debiasing or just fail to understand what they are.

A large part of the problem is that all the lessons of Traditional Rationality teach to guard against actually arriving to conclusions before amassing what I think one Sequence post called "mountains of evidence". The strength and stridency with which LW believes and believes in certain things fail a "smell test" for overconfidence, even though the really smelly things (like, for example, cryonics) are usually actively debated on LW itself (I recall reading in this year's survey that the mean LW-er believes cryonics has a 14% chance of working, which is lower than people with less rationality training estimate).

So in contradistinction to Traditional Rationality (as practiced by almost everyone with a remotely scientific education), we are largely defined (as was noted in the survey) by our dedication to Bayesian reasoning, and our willingness to take ideas seriously, and thus come to probabilistic-but-confident conclusions while the rest of the world sits on its hands waiting for further information. Well, that and our rabid naturalism on philosophical topics.