The problem is that self ID makes the sex based exemptions much harder to use because when a person has changed their legal sex and gets all the privacy protections that come with a GRC, applying the sex based exemptions would usually have to depend on a trans person saying they are trans. (Think of a girls group that has female only staff, they are legally female so apply to volunteer, yet may be fully male bodied. This can't happen with transwomen without GRC's.)
And the considerations re discrimination are effected as well, for example the comparator class of a transwomen who has changed their legal sex to female becomes female and not male, and this can impactson how discrimination is understood, for example if a transwoman with a GRC has their request to be moved to a female prison refused, and they claim unfair discrimination, in judging the case their comparator class is female, and thus their lawyer only has to argue that they are being treated less favourably than female prisoners. Without a GRC, their comparator class would be male, and they'd have to argue they were somehow being treated less favourably than male prisoners. A lawyer recently wrote a blog about it. Although with that said, the exemptions are still applicable to transwomen with GRC's, so this would still factor in, however it may factor in differently.
So the EA sex based exemptions can be applied to all trans people, with or without GRC's, but with a GRC they are harder to apply due to what comes with a legal sex change, and their legal sex change may also affect the question of what is proportionate and legitimate.
All of this is already a problem. Self ID turns that into a huge problem because it's gives all of this to anyone who identifies as a woman, or at least say they do.