Secondly, if you think that "under Self ID" people can change their gender daily, on a whim, you haven't understood self ID, which is odd given that you have recently seen what such a law looks like in Scotland.
IIRC there have been long and protracted discussions. Waking up tomorrow and saying I am a woman and I demand to be treated as such is the holy grail of self-ID. For the purposes of equality law no piece of paper is required to say that you *are* a woman. If you say you are, then you are. That is self-ID.
That is different from legal gender recognition which requires a piece of paper.
Where I actually agree with you, is that in the vast majority of places I don't think it matters. If you decide tomorrow that your name is Stella and you go out to a restaurant wearing a cocktail dress, and use the ladies loos, it doesn't matter. It also doesn't matter if your name is bob, you have a shaven head and skull tattoos on both arms. What matters is whether you are going in there to use the loo, washing your hands and then leaving, or whether you are going in there heaving out your junk and waving it around in the faces of the other occupants of the toilet.
As you and
@monkers have pointed out previously, the protection in toilets is legal. If an offence is being committed and offence is being committed whether it's in the ladies or the men's.
The issue is one of custom and the impact on other users. Personally I would not want to interpose myself into a space where it makes other people uncomfortable. I have used ladies loos on a matter of principle when my daughters were little because it tended to be where the baby change mat was.
A secondary issue of course is for those people who are genuinely trans, and likely therefore to feel uncomfortable in either bathroom.
Rolling back from the digression, under the principle of self-ID (not legal gender recognition), a good question would be "what are the issues (if any) that this represents?"
Without legal recognition, many of the protections that women enjoy remain in place. With legal recognition some of those become contentious IMHO.