The 'how taf do we deal with a very obvious bloke insisting he's not a bloke and waving legally false information while still fulfilling our duty of providing sex based provision for women that's free of men, harassment and a choice between submission to belief or exclusion, and without paying a fuckton to them in court' advice is what's wholly missing from the guidance. That's going to be important.
Yes. This is important. This gap in the law - that lets people change their sex markers on government ID while making people's sex important legally for organizations to be able to know - puts organizations in an impossible situation where they feel they they are going to get dragged through the media gutter and sued if they do what they are supposed. And the EHRC, who are supposed to make things clearer for organizations, have completely ducked on the one thing that isn't clear with the SC ruling - how to implement.
The EHRC is utterly useless on this point. And it's exactly where they could have put hepful strategies for organizations. A) pointing out clearly that if it's inappropriate for a place to have people who look the opposite sex in there (because users would reasonably be distressed by having to share with someone who they reasonably believe is the opposite sex) then that person can be refused access (though may need to be give access to a third space).
B) where it isn't appropriate but is necessary for qualifying someone (for an award, say) instead of saying that asking for identity documents is not appropriate as they may not show true sex. They could point out that a birth certificate will show the true sex for the vast majority of people (as most trans people do not have a GRC) and (as I understand it) there is one way to check if the birth certificate is of an original birth record, at least for people born in the UK. The GRO indices (one for England and Wale, one for Scotland and one for Norther Ireland) are indices of births at the time of registration and are not changed when a GRC is issued (a new entry is made on a private index for holders of GRCs). So someone who actually is male will either have that on their birth certificate or they will have a GRC, have female on their birth certificate and they will not show up on the public GRO index.
GRCs aren't the only reason for people's birth certificates to not show up on a GRO index, but it's not common with, I believe, adoption (at about 4,000 registrations a year) the largest share by quite a way.