She is not circumventing any rules. You cannot be forced to join AEA. She will be working on an Equity contract, she will have working dues deducted and benefit trust contributions made on her behalf. She will just not, herself, be a member. Her quitting the union was extremely performative and really only saved her the twice annual membership dues, which is a negligible amount for her.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."