Sechel Hayashar: I know exactly which family you mean, and they are indeed a verry choshuver family, but it only goes to prove my point. They came from outside, although not to far away, and they were told to keep their levush because it makes it obvious to anyone who sees them that this choshuve family were attracted to Lubavitch from the outside.
My challenge, I suppose it could be called, was to find me someone who was told to keep his mesorah when it would not be so obvious that he was choshuv and/or from the outside, for example, to keep winding tefillin the other way, to keep wearing non-lubavitch tallis/tzitzis. Do you know anyone who was told to keep their mesorah where it wouldnt result in people being impressed with their being attracted to lubavitch?