Mr Kassam tweeted said to Mr Oluwole: “Soros (your boss) isn’t a Jew and helped Nazis round up Jews. You work for a Nazi accomplice.”
Mr Wigmore added: “[The] fact is it’s the @UKLabour who hate the Jews not us, we have always been pro Israel, I fail to see how using @georgesoros as an image is anti-Semitic, he’s not Jewish and was a Nazi collaborator, he admitted it.”
Both tweets have since been deleted.
The Board condemned the pair, accusing them of “knowingly or not… spreading false antisemitic conspiracy theories about George Soros being a ‘Nazi collaborator’.”
A spokesman added: “While there can be legitimate differences of opinion on Mr Soros’s politics, holding a 14 year-old Jewish boy responsible for the atrocities perpetrated in Nazi-occupied Hungary, is the ultimate in victim blaming.
"They should retract and delete these comments.”
Mr Kassam told the JC: “As the Israeli government recently pointed out, left wing activists leveraging antisemitism to defend the destructive policies of a Hungarian-American, pro-open borders billionaire atheist, is wrong.
"Soros hates Israel, and as my historic work with the BoD and indeed for the JC has shown, I will never countenance the destruction of Israel. No matter how much some at the BoD now seem to want it.”
Mr Soros, a world-famous investor and philanthropist, was born to Jewish parents in Hungary and lived through the Nazi occupation.
His family hid their Jewish identity as a means of survival, acquiring identity papers, and helping others to do so.
His funding of liberal political actors has made him the target of nationalist and far-right attacks, many of which have been antisemitic.
A package containing an explosive device was found in the post box of his New York home in October 2018, but was detonated by bomb squad officers.
