Haldane's decision seems to have been widely accepted by the UKGovt
As said up thread and on numerous occassions, it wasn't that her "decision" was accepted, it was that her ruling was in line with the existing practice of the law. ie "for all purposes" trans women are women unless the situation it one that is covered by the EA exemptions.
So the court case changed nothing except that a few newbies to the issue realised for the first time how the inclusion of gender reassignment (not gender id) had been given precedent over actual women. Also confirmed on the Jeremy Vine show by Ayesha Hazarika who helped draft the EA.
That is why at the time Nicola Sturgeon and others had no problem with the outcome of that court case because it changed nothing.
In fact many women were puzzled as to what the purpose of the court case was unless it was a stepping stone to have the case heard in a higher court.
And I am sure many Judges would be horrified to think that they would tailor their decisions based on what might please politicians.
But more importantly as the case is being heard in Scotland where any number of groups were allowed to break the EA by saying that trans women could not be included by single sex service providers, or indeed appoint a trans woman to a post advertised under the EA as women only, the inferrence is that the Scottish legal system is quite happy that trans women are treated as women.
And if there is some independently minded Judge in the Scottish Legal system does overturn what is the accepted legal interpretation of women in the EA throughout the UK, I suspect for it to become actual Law would mean another court case in the UK High Court.
From 2011 UK supreme court's jurisdiction in Scotland upheld by review panel
(I tried to find updates on this but was hampered as for some bizarre reason google has removed the search by date range option - bonkers!)
As I said upthread, this many have been the legal strategy of which ever legal team is advising FWS, but in view of the amount of money already spent on this, and the current fund raising, it might be better if they were a bit clearer or transparent as to what they are hoping to achieve via Scottish Courts.