The fact that segregating or even bloody distinguishing TW from sex offenders, cross dressers, autogynephiles and any bloke who feels like it is impossible, is one of the main reasons why women need single sex spaces.
Let us remind ourselves of Stonewall's definition of trans. It wasn't feminists who created this:
An umbrella term to describe people whose gender is not the same as, or does not sit comfortably with, the sex they were assigned at birth.
Trans people may describe themselves using one or more of a wide variety of terms, including (but not limited to) transgender, transsexual, gender-queer (GQ), gender-fluid, non-binary, gender-variant, crossdresser, genderless, agender, nongender, third gender, two-spirit, bi-gender, trans man, trans woman,trans masculine, trans feminine and neutrois.
They don't exclude sex offenders. They specifically include gender-fluid (aka men who say they are women part-time) and cross-dressers (aka transvestites).
Let's remind ourselves of the definition of woman:
Adult human female
We can READ!
You explain which definition is more confusing and harder to maintain single-sex spaces with: figuring out which of the men who say they are trans is "legitimate" (a false question, because Stonewall says they all are), or just keeping women-only spaces for biological females?