I was brought up with two religions: Lutheranism and Judaism. In Jewish law, your mother must be Jewish to be considered a Jew, and my dad is the one who is Jewish so therefore I'm not really considered to be a Jew. I never was Bar Mitzvah'd either. I don't believe in a god, however I respect others who do and it is not my duty to tell others what they should and shouldn't believe in.
If I had to belong to a religion though, I'd probably become a non-denominational Quaker. If someone asks me what I am though, then I just say I'm a Jew.
Also Zionism is not a religion, it's a belief that some Jewish people believe that Israel is the homeland for us. It's relatively new as well, which started in the early 20th century. As someone who considers himself to be a Jew in a cultural sense, I do not support Israel in regards to it being an exclusively Jewish-state, as that is just racism. Especially since most religions consider Israel to be their "homeland", namely Islam and Christianity. Then again, Muslims and Christians are free to practice whatever religion they want in Israel, even 20% of the Israeli Knesset is Muslim which says a lot. While the intent of some of Israel's first Jewish settlers was to create a Jewish homeland and that does imply racism, that is most certainly not the case as Israel is pretty much a religiously-balanced society.