Zionism is not a nationality, Hyde. Zionism is an ideology. Besides being Zionists Israeli citizens can also be anti-Zionist, non-ideological or non-Jewish Palestinians, Armenians or Russians.
I know quite a few Israelis in NYC who are musicians and do not have any ideology (they were born in Israel). It is another question whether they find courage to stand up to Zionist atrocities by Israel, but they are certainly not Zionist. My doctor is an Israeli Jewish who was born there, native Hebrew speaker. He is also not a zionist and does not refuse to treat me if I wear a keffiyeh. You might think that Israeli means the one who came to colonize and live on Palestinian land by choice, but it is not so at all.
Many Israel-born Jews woke up and started to work towards people's equality against Zionism and racism in various organizations and in journalism.
To see an Israeli or a Jew wearing a star of David and to believe right away that this is a Zionist, regardless of what he-she does or says, that this is a racist, a fascist and a former perpetrator of atrocities is BIGOTRY.