Many in Israel see a Jewish identity drawn in different lines than religious or traditional ones. the Jewish people are historical people, a people who took part in collective political and social endeavours on a national level. Judaism has been the religious dimension of a Jewish nation or culture, perhaps in the same way that Shintoism has been for the Japanese nation.
in this regard, as Israelis we base our identity on aspects which are distinct to our experience. such as understanding modern Jewish history, participating in military service, etc. in this regard, in modern times Jewish identity has transformed from Torah studying to social activities.
The Israeli experience forces you to hold some sort of Jewish identity, even if you are critical of it. in this regard secular Israelis who criticise the religious establishment in Israel, will show a coherent knowledge of Jewish teachings. sometime they would even display how the rabbinate in Israel distorts what are otherwise humane Jewish teachings.
I think it is on the same level that if I was born in India, I would not practice Hinduism, or if I was born in Sweden, like many other Swedes I would not practice Christianity.
I have a cultural interest in 'Jewishness', and I think that this is one of the greatest advantages Jewish society has in this regard that it goes beyond what many people in Europe experience today, it seems that they have a disconnect from historical Christianity in all its brands. while many secular Jews have an affinity to the Hebrew scriptures, to various Jewish teachings, customs, or philosophy.
I think that the success as I understand it of many American Jews to preserve a healthy Jewish identity has been in the way that through modern history they have developed a successful liberal experience, they are Jewish in faith and culture, but they have a solid social structure, they probably have a strong sense of community, and I think that unlike many Israelis who are frustrated by the way that the religious establishments have a hand in domestic politics, their experience has probably been largely positive and supportive.