This is a very real and very legitimate problem to be solved.
Surely, you must feel perfectly comfortable walking around naked, having people watch you defecate, or having sex in public? After all, it's part of life!
The whole reason we all agree that having a locked room to do your business in is ideal is because it's such a vulnerable position to be in. We feel better about being in a locked room, but you can never get your basic instincts to not feel vulnerable when you're mid defecation/mid urination. It's animalistic and can never go away.
Quite literally, knowing people can hear us take a dump triggers survival instincts because our brains think we could be alerting predators to our whereabouts while we're not in a position to run or fight
I'm not sure that's true. Given enough time it could change. I'm just not sure why we'd want it to. I'm perfectly content to leave some things a mystery and that includes what anyone else is doing in the bathroom.
I think it's also highly dependent on your cultural background and upbringing.
Doing your business next to a stranger in Tevas with hobbit feet and a serious gastro intestinal issue is nightmare fuel for me.
Looks like the actual number is somewhere closer to 2.8% - 16.4% of people [https://pubmed.ncbi.nlm.nih.gov/28554367/]. (This study was specifically about "shy bladder" but that seems a pretty close proxy)