My experience in Ireland is that the average person does not believe in gender ideology at all, isn't aware self-id exists in Ireland, is quite skeptical of the idea of trans children, and has a vague "sure what harm are they doing" view of adult trans people that falsely assumes trans = dysphoric post-op transsexual. As soon as it becomes clear that trans = anyone who says they are, the average person is immediately opposed to males in women's spaces (sport, prisons, rape crisis or domestic violence services, etc.). Similarly, as soon as they find out that puberty blockers aren't harmless pause buttons, they're against allowing children to transition.
This kind of view is very clear on Irish online anonymous forums like boards.ie, heymammy/rollercoaster, PROC, etc., and in select conversation with people irl. I've noticed that sport (esp. GAA) is often the peak trans moment for men, and prisons quite often for women. This view doesn't appear so visibly on named social media like FB or Twitter because of...
...Pockets of wokery around the country, including certain geographical areas (esp. middle class Dublin and other urban areas, which encompasses the entire staff of the IT and RTÉ, and many of the activist organisations that are now all TWAW), random cliques around the country of secondary- and university-age students (often centred around trans students they know), and individual people who get their socialisation online via social media (Instagram, tiktok, Twitter for the older folks) as opposed to via irl interactions.
The vociferous nature of these pockets of wokery is quite successful in stopping the first, larger group from speaking openly when they're peaked by the latest Barbie Kardashian or JKR pile-on or whatever.