Ms Moran, whose mother was born in Jerusalem, raised the example of the posters that were put up around London, after Labour belatedly adopted the International Holocaust Remembrance Alliance (IHRA) definition of antisemitism, that said "Israel is a racist endeavour".
This was intended to mock the definition, which cites these words as an example of potential Jew-hate.
Ms Moran said: "When you see posters go up, it takes so long for the top of the party to be able to say 'no, that is antisemitic'."
She added she "essentially had to explain" to John McDonnell why they were antisemitic when they both appeared on the BBC last September.
Ms Moran was applauded as she told the Question Time audience: "It does nothing for the Palestinian cause. My plea to those who feel they need to step up for the Palestinians: Please do that, my God do we need it but also please don't do it in a way that stokes antisemitism.
"You can do both. You don't have to be pro-Palestinian and antisemitic."
