I think a lot of people, and as (from your story and our experiences) frum people too/especially do not really understand what it means to be a “Chosen” people. We need to act(myself included) like what we ‘chosen’ to act like and not feel like we are more important than everyone else, although our mission in life may be.Unfortunately it seems that too many Jews think that we can do whatever we want because we are “tight” with Hashem and it does not really matter what others (goyim or the non-frum )think, because ‘who are they?’
I am from a BT family(they became so before I was born)and I try to act in a proper(G-D fearing) manner when near non-Frum relatives because they are under the impression that all frum Jews act in the manner you described above. The best way to fight it is to disprove it.
One thing I may suggest to help the ‘fight’: say hello to goyim or the non religious when walking to shul or wherever. It makes a real difference.