My rules:
No shoes on inside the house.
Socks stay on. (I've never had an issue with it)
Closed toed shoes in the summer/socks put on upon entering the house.
Water shoes for water play
But those rules are something I have eased up on over the years but some will remain forever.... such as no shoes in the house. Shoes in the house is gross.
I had a rule about kids wearing socks but to be totally honest, I used to have a lot of families that were less than what I'd call clean so... now it's not such an issue for me, but I personally think feet are kind of gross. (my sister buys shoes at garage sales for herself and her kids etc....I could never. eww!) So I prefer socks but don't necessarily require them.
Closed toed shoes in the summer is strictly a safety issue. Kids trip over sandals and those stupid Crocs (did I mention how much I hate
Crocs )
This year I am considering requiring actual running shoes (with laces) and not just closed toed sandals as those sandals are starting to be a pain in the butt. Sand gets inside of them and the kids are constantly needing to sit and take them off to dump them out and that gets cumbersome all summer. Especially since the sandbox is a major playground attraction.
Still no matter what, I do not allow the kids to wear sandals, Crocs or go barefoot. All for safety reasons.