Yes all pools are fine for that kind of physical disability. All the ones I have ever been to have provisions for wheelchair users in the standard shower room, for example.
Children who grow up in Iceland are highly unlikely to develop phobias and body issues around the swimming pool because it is such a normal and everyday part of life and they see people of all kinds in the changing rooms, including those with disabilities and physical differences - people of all ages, shapes and sizes.
Of course it could happen in various circumstances that people develop fears of normal things in any society, but therapy to overcome that is a more practical course than expecting society to change. It's certainly not a common issue that people living here find themselves unable to go to the pool.
As for why it's communal rather than separate cubicles, well it's much more cost effective. Money is better spent on maintenance and cool slides than putting in expensive and space-inefficient cubicles.
After living in Iceland for over a decade, I find the grossness and lax hygiene practices in UK pools off-putting and I probably wouldn't go to one again. I can also well believe that ND people from Iceland would find it hard to deal with a UK pool. But that's life, isn't it, different countries do things differently, the UK isn't about to start improving pool hygiene practices because everybody there is just used to the way it is. When you're a visitor or a recent immigrant, you just have to take things as they are.
Having said that, because mass tourism is so big in Iceland, generally if you keep to the pools that are closer to the centre of town, you are quite likely to find that some concessions have been made for tourists. I think another one that has some shower curtains is Vesturbæjarlaug. But they don't have any slides so I wouldn't necessarily take kids there! It's pretty boring, but a good pool for chatting and chilling because they have a massive hot tub area.
You won't get the best slides or views in the more tourist-focused pools, but you can still have fun 😉