Asked if the man was welcome in the Labour Party, Ms Long Bailey said the disciplinary processes of “cases of clear cut antisemitism end in immediate expulsion”.
Interviewing her on BBC 2 on Wednesday, Mr Neil also questioned her about whether she had “stayed silent and went along with those that opposed” the adoption of the IHRA’s working definition on antisemitism during a debate on Labour’s governing National Executive Committee in July 2018.
She said: “I don’t believe that adopting the IHRA definition and examples ever went to a vote because we all agreed on the NEC that it should be enshrined within our rule book and our procedures.”
When pressed repeatedly, Ms Long Bailey said that she “can’t remember now” whether she had spoken in favour during the debate but that “I adopted it and I fully supported it”.
“I have never been silent about our lack of – of our handling of the antisemitism crisis,” she said.
Ms Long Bailey has sat on Labour’s frontbench in 2015, and has been Shadow Secretary for Business, Energy and Industrial Strategy since 2017.
The exchange was part of a two wider interviews in which Mr Neil quizzed Ms Long Bailey and Sir Keir Starmer, the frontrunner to be the next leader.
Ms Long Bailey, who has had to deny she is the "continuity Corbyn" candidate, is standing against Sir Keir and Lisa Nandy to be the next Labour leader.
The results will be announced on April 4.