Instrumental in the formation of groups such as Jews Against Zionism, and once closely linked with expelled Labour activist Tony Greenstein, Mr Rance opposes the IHRA definition of antisemitism.
One Jewish Labour member in Enfield said the decision to invite him "feels like an attack on me" and said it sent out a signal that the only Jews welcome in the Party were those who were "virulently anti-Zionist".
Meanwhile in Chingford, the JC has been forwarded a copy of the agenda for the CLP's November 26 meeting where JVL founding member Naomi Wimbourne-Idrissi has been invited to speak "on antisemitism."
Ms Wimborne-Idrissi once used a speech at a Manchester Labour meeting to dismiss the vicious abuse sent to Luciana Berger and other Jewish female MPs, saying there was "no proof anybody in the Labour Party is going to punch them in face”.
She also called questions over Mr Corbyn's attendance at a wreath-laying ceremony for Black September terrorists "absurd".
Mr Caplin said: "It is deliberate obfuscation for the Labour Party to claim that antisemitism is under control, when local Labour parties in some of the most heavilyJewish populated constituencies give platforms to those who deny antisemitism in the party exists and affiliate to organisations that defend those who have been suspended or expelled.
"It is hardly surprising there is distrust from the Jewish community in Labour when local parties appear to put the interests of antisemites in the party above the interests of Jewish voters, supporters, members and the wider electorate."
Mr Greenstein was allowed to speak from the main platform at a JVL meeting in Liverpool during Labour's annual conference in September despite his expulsion over allegations of antisemitism.
In a move that sparked outrage amongst the majority of Jewish members, Hornsey and Wood Green Labour branch voted to affiliate with JVL last month.