Independent Jewish Voices says equating anti-Zionism with antisemitism amounts to an appalling capitulation to pro-Israel groups.
Polanski, who is Jewish, faced heckling after describing Zionism as a form of racism during his byelection campaign in Holborn and St Pancras, the Guardian reports.
The Al Jazeera series Deja Vu examines the movement's stance amid centuries of Jewish-Muslim coexistence.
A proposed policy for debate at the Green Party's October conference has prompted calls for leader Zack Polanski to clarify his stance, amid concern it could alienate Jewish supporters.
A new Al Jazeera World film looks at Neturei Karta, an ultra-Orthodox Jewish movement that opposes the State of Israel on religious grounds and has voiced support for Palestinians.