It's normal in restaurants that aren't fast food

They're supposed to wash their hands and wear gloves. And, at least at the ones I work at, there are boxes of gloves at nearly every station so there's no excuse to not have any on.

No its not normal. And it was an easy way to get fired at the restaurants I worked. Zero tolerance rules on food safety.

I don't think there's a single state in the US that allows you to make food without gloves.

The only exception I've seen is when you're dealing with the ingredients before they've been cooked, like with pizzas.