HaLeivi > This whole idea — that simply doing any Mitzva openly, even when it’s despised, is a Kiddush Hashem — seems to be a reaction to the opposite idea, that we should be ashamed of Mitzvos deemed inappropriate by the outsiders.
I think you are right that we often stand by a point to separate ourselves from others. IT is often important to protect community in a short term, but, in a long term, distorts who we are. One example I saw quoted is emphasizing that Judaism is a religion of actions/mitzvos rather than stam belief (from lo lishma, etc) that we affirm in the face of neighbors who insist on being saved through faith. Similarly, emphasis on miraculous in the face of haskala rationalism.