It seems that TWAW for the purpose of playing on women's teams regardless of level of gender reassignment (whether GRC holder / medically / socially transitioned). Also it seems that none of the sporting bodies are using the allowed discrimination stated in the EA when it comes to making sporting events fair competition and safe for all participants.
But if a club uses 'Gender reassignment is a protected characteristic' as a reason why it is perfectly acceptable for a person born male to play on a women's team, why are they not then falling foul of the EA by excluding a female born person and therefore allowing discrimination under the protected characteristic of sex?
There's probably a really obvious answer, but I can't see it at the moment!