Three actors donned the Palestinian keffiyeh at the end of the opening night of the company's production of Chekhov's The Seagull on Saturday.
The move sparked criticism from the Jewish community, with the chairman of The Haus public relations group, Judi Hausmann, reportedly resigning after 16 years on the STC board.
Ms Hausmann chairs the STC's Remix organising committee and is one of the company's foundation directors.
The Sydney Theatre Company and Ms Hausmann have been contacted for comment.
The National Council of Jewish Women Australia posted online that the STC was loved and supported by many in the community, and had failed.
"You have failed on a deep and moral level. We cannot forget this easily," the post said.
The Media Entertainment and Arts Alliance said it would support any members disciplined by their employer for expressing their views.
"MEAA respects the rights of members to publicly express their views on this issue, and will support any members who are subject to disciplinary action for simply engaging in freedom of expression," said acting chief executive Adam Portelli.
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