They do have protections against that in the contract, which would apply to all SAG members — the use case you brought up is exactly what Fran Drescher, the president of SAG, brought up of something they are hoping to prevent.

The studios don’t want to sign such a contract. And so the actors are withholding their work until they do, among other conditions. Crossing the picket line, no matter how big an actor you are, will have you expelled from SAG, and when studios eventually sign whatever deal they do with SAG, any non-SAG actor will be barred from working with studios, based on the exclusivity contract that’s been in every deal since 1960.

One side will win. Based on history, it will be SAG.