A propos self-ID in Ireland causing no problems: As I recall, the legislation was also snuck through the back door - no referendum or anything. Women weren't given a say.
^ this.
The Irish people I've mentioned it to have absolutely no idea it has happened, and what it means. In most of Ireland it's the way the UK was 5 - 10 years ago, before "trans" became a talking point. The way most of the world is.
I live in a rural area of Ireland and the reason there are no problems here is that a) people don't know b) would be horrified (at women sharing spaces with men) if they did know and c) transwomen in this area are rare -- I've never seen one.
I go to a leisure centre where there are separate changing areas for men and women. I can just imagine what would happen if a male-bodied self-IDed person decided to change along with us middle-aged ladies as we strip down and chatter with each other.
I doubt if any one of these ladies have even heard of the issue of self-ID, much less agree with it. I only know because of my background in media and women's rights, and because I moved here recently.
If there are "no problems" it's not because Ireland is so woke. It's because most of Ireland is still sane and still unaffected, and this legislation has been quietly snuck in without them knowing what it is and of the consequences.