How to overcome preconceived ideas about social scientists?
I get patronised by the guy whose randomised experiment allows him to
  get away with a t-test. How to react when that happens without
  sounding too defensive?


I think this is the key aspect in your question. Once the "hardsplainer" starts patronizing you, you are on the defensive. And there is really no good way out of this situation once you react by starting to defend your methods.


Sometimes the hardsplainer will realize that his assumptions were erroneous and that you may indeed know more about stats than he.
Or he will in turn get defensive and start nitpicking your methods, probably getting in deeper and deeper water as he is discussing stuff he may not know much about. This is not a good conversation to have at social gatherings.


I'm afraid the second possibility will happen rather frequently, simply because people are not good at revising preconceived impressions.

So I'd recommend that you nip the problem in the bud, by not allowing your interlocutor to, in fact, preconceive the impression of "look, a social scientist, who probably doesn't know anything about statistics". Specifically, when you discuss your work, invest half a sentence to name-drop your analysis techniques.


  I'm looking at how foo relates to bar. Because I only have
  observational data, not experiments, I use econometrical panel data
  models, and I find that...


If you hint that you use advanced models right before the hardsplainer can get the wrong impression that he can lecture you with fundamentals, he will be stopped cold. (Of course, you don't want to overdo it to come across as an arrogant know-it-all.)



Yes, it would be nice if this were unnecessary, because people didn't have the preconceived notion that social scientists are inept in terms of statistics. Unfortunately, this notion does have a basis in facts. I do statistics for psychologists, and I see that while they do get a solid grounding in statistics, they do frequently misapply models, or interpret them incorrectly, or don't understand why p-hacking is a Bad Thing. Then again, some hard scientists do suffer from the delusion that being an expert in some hard science means that they automatically also are experts in statistics.