I think that sometimes weird looks are more looks of curiousity, not anything more sinister. You're doing something that doesn't conform to the norms, so you'll attract attention by default.
That said- a lot of businesses near where I am have "no shirt, no shoes, no service" policies. I'm not sure where the "no shirt" taboo came from (probably poverty-taboo-related, sure)- but the "no shoes" one does at least have some basis in disease transmission. There are diseases and parasites that love bare feet, as a couple of commenters point out above (plus the standard plantar warts, athlete's foot, etc). There's also the liability issue- if you are on someone's property and there's a bit of glass or something else that cuts you, they're liable (they have a responsibility to keep their property safe- tho they could fight that if you drop a knife/glass/etc on your own foot). If it cuts you, you get blood on their floor, and they have to clean it up- they have to follow blood-borne pathogen rules. If you happen to have a disease, and someone else trods in your blood- perhaps also with an open wound (burst blister, whatever)- then that's another problem.
So- even though I'm all for straight-up bare feet in more natural areas- areas which can deal with these nasties through their local ecosystems, and there's no possibility that anyone would think it's a sterile/safe surface- I'm all for things like Vibrams or flipflops or huraches in urbanized (or, ugh, even worse- suburbanized) areas. Furthermore, I'm even kind of twitchy re: lawns- those are not natural ecosystems. They're usually chemically-treated within an inch of their lives, and I've no desire to pick up more herbicides/pesticides than necessary.
Honestly- foot protection is a product of living in a community of more than ~150 people. The current inability of most people to live in groups this small without ridiculous externalities (sprawl, pollution, etc) is a result of overpopulation. The norm is to wear foot protection because you (or perhaps, the average person) literally cannot trust your neighbor/coworker/shopkeeper (the average local-geography-community-member) to not have transmissible parasites/diseases or have sprayed their flat surface with some chemical nastiness.