I'm not sure that the WI is going to get on board without a very clear and concise explanation.
They, rightly in my opinion, welcome men "Who live their lives as women". And, as far as I know they aren't the core issue, indeed, from experience here and in RL, many trans women would be more than happy to get behind the anti Self ID proposals.
BUT, and it is a big BUT, I suspect that they would only get behind the 'talk to us all before you seek to re-write biology' issue if it were explained very clearly, from a scientific basis, with the medical issues outlined - that is the gynea services like breast screening etc. Maybe event he medical treatments for young kids, the concatenation of sex with gender, etc.
That could lead them to decide to do more, but going in with the 'threat' aspects would probably make them back off, as they are all about inclusivity.