We probably should define a “Jew” as someone who at the least in Shomer Shabbos and Shomer Kashrus (and just those two sets of mitsvos more or less preclude being part of “normal” American life). If you throw in things such as dressing frum or a man having a beard and pe’os, you will discover that there are almost no Jews in political office outside of low level positions serving districts that have a high percentage of frum Yidden.
It is probably in out interests to let the (increasingly non-Jewish) descendants of Jews identify with the Jewish aspects of their heritage since that precludes the “racial” anti-semitism that led to the holocaust.
That non-frum Jews celebrate Hanukah is amusing, since the holiday celebrates a war in which the frum Jews defeated the secular Jews (there was no racial anti-semitism back then, the Greeks loved assimilated Jews,it was only frum Jews who were persecuted). But we should probably not say that when the secular Jews are listening (why pick fights when you don’t have to).