What “hygiene reason” are you thinking of? In the general case it doesn’t seem any more or less hygienic to touch the bottom of my shoe to the library floor vs. the bottom of my bare foot. Both are going to be comparably dirty if I walked in off the sidewalk (the foot is probably a bit cleaner on average).

If the worry is something like fungal or bacterial infections of the feet, those thrive in the warm, wet environment of a sock/shoe, and can’t survive when consistently exposed to fresh air and sunshine.

If the worry is injury/liability, then high-heeled shoes would be the obvious first thing to ban. Those are dramatically more dangerous than bare feet in basically every context.

I suppose if someone had gaping sores on the bottoms of their feet it might leave gross/contagious residue? But someone could just as easily track vomit, feces, cake frosting, rotten food, chewing gum, or whatever other yucky thing in on the bottom of their shoe. The “has a serious contagious skin disease” case seems like it would be handled better with a more targeted restriction, since I don’t think you want such people’s hands touching stuff in public spaces either.

My guess is that the real reason is to keep barefoot, shirtless, etc. homeless people and/or hippies out of public buildings. There are also rules against lying down, being drunk or intoxicated, making loud noises, bringing luggage or carts, communicating “willfully” or obscenely, emitting strong odors, &c. I’d be curious to learn more about the history of restrictions against bare feet in particular.

> the bottom of my shoe to the library floor vs. the bottom of my bare foot

The hygiene of your foot, not their floor, i.e they don't want you walking on their (relatively) dirty floor bare-foot.

Also, if they allowed others to walk in bare-foot, gaping sores etc would make the floor dirtier.

I'm pretty sure they don't "allow" you to vomit on the floor, or throw rotting food onto it either, but if you did that (unintentionally?) I'm sure they would clean it up and disinfect the floor, for hygiene reasons. That people might track those things in in trace amounts is why the floor is considered dirty, and why it is probably cleaned periodically.

I wonder how much cleaner my shoes are than me feet. I wash my feet at least everyday, but seldom wash my shoes.