Can someone "explain like I'm 5" what the issue is? I wear shoes and socks like any normal person does, but if I saw someone barefoot at breakfast I wouldn't be offended by it, I would just think it's weird and potentially kind of unsanitary for the barefoot person. But I don't get how it affects me? What difference does it make if people are walking around with their nasty bare feet instead of their nasty shoes that have stepped in who-knows-what outside?

My understanding of the "no shoes no service" signs is that they have their origins in anti-hippie discrimination and that, apart from a few towns in New England, there aren't any state/local or other regulations requiring shoes in restaurants.