Mr Parsons said he later recognised Mr Tobasi as one of the group when he saw photos from the play's performance. He said he reported the incident to the police.
A WMFI member who wanted to remain anonymous said Mr Tobasi shouted abuse at her and her friend while they were handing out flyers on the Saturday night. She said: "He started ranting 'You will die soon, you will all die. I have no problems with Jews but you Israeli Zionists, you have blood on your hands.'"
The Freedom Theatre denied the allegations. In a statement, it said: "The theatre does not tolerate any violations of human rights or any acts of violence by our staff or members. We strongly refute accusations of racial or any other abuse committed by any member of our company in connection with the performances of our production The Siege at The Birmingham Rep."
Ruth Jacobs, head of WMFI and chairman of the Representative Council of Birmingham and West Midlands Jewry, said she was "so sorry" that Christian friends who had helped give out the leaflets "had to experience this nastiness and intimidation".
West Midlands police said they had logged Mr Parsons's complaint as a hate incident but would take no further action.