I'm going to regret posting this but here it is as someone who grew up in this community:

Jewish can refer to three things: religion, race and culture.

There is the Jewish religion, which basically adheres to the Old Testament. It changed a lot since the fall of the temple in Rome. You can convert to this if you want. You can be born into this and ignore it, become an atheist.

There is the Jewish race, Asheknazi and Sephardic. Basically, a group of people who are genetically similar, having bred together for a long time. Prone to certain diseases, genetic markers, etc. This is obviously something you're born into.

There is the Jewish culture. Varies by geographic region. Latkes, lox, bagels and shit. Tends to come along with the other two. People might reject the religion, but embrace this. I do, bagels and lox are tasty.

Zionists are people who support the Israeli apartheid. Now here's the interesting thing: A lot of people who are racially/religiously Jewish think this is pure bullshit. Especially liberal Jewish people. My facebook has been filled with 'I'm Jewish but fuck Bibi' lately.

Here's the other interesting thing: A lot of the strongest 'Zionists' in Israel are not very 'Jewish'. They are secular. They are, I suppose, racially Jewish, but don't go to temple or believe in God. The orthodox Jews and military-leaning secular Jews in Israel actually get pissed off at each other on a regular basis.

Every defense I've seen of Zionism has been rooted in the religion, so I'm not quite sure what the deal is with the secular military types. I did notice this being indoctrinated when I was younger in religious school. I actively rebelled against and it quit (20+ years ago).

So in brief summary: Most Zionists are racially Jewish, but not necessarily religiously or culturally Jewish. Many US Jews, being fairly liberal, think it's a bunch of bullshit. Most Zionists I know of are conservative religious Jews or living in Israel. At least 20+ years ago, this shit was pushed in Hebrew schools.