"You cannot just randomly pick out someone who is not harassing your customers or staff and throw them out."
Then essentially, it's not your business. If somebody is taking up space in my place reserved for a paying customer, I'll give them the boot. I'm in business to make money, not out of some obligation or agreement to provide some "public accomodation". It's my credit, my money, and my time invested, not the government's.
"No shoes, no shirt," etc. is a health concern and need not be posted anywhere that I'm aware of. If a health inspector walks in your restaurant and sees a customer without shoes, you are likely getting hit with a violation.
None of that is the issue here, though. The issue is some goof writing a law because some guy got thrown out of a bar.
It says he was there with his wife and friends who seem to have been drinking. The bar owner was a damn fool to throw out one person in a party of many. I can only hope my competitors all think like you.