There isn’t a way to woke-ify gender segregation, btw. “Single gender/sex spaces” always have been and always will be exorsexist, misogynistic, intersexist, and transphobic.
And changing the language from “women only” to “non men only” to try to make it sound less TERF-y doesn’t make it any less bigoted. Think about it. There’s no way to actually enforce a space being strictly “female only/women only/non men only” without relying on regressive stereotypes or assumptions about the complexities of other people’s gender experiences (or lack thereof), and there’s no way to create a “female/women/non men only” space without implicitly inviting everyone in the space to go around questioning whether anyone coming to the space is “non man enough/woman enough” to exist there, creating an unwelcoming environment for anyone who isn’t strictly gender conforming.
