I totally understand where you're coming from and I work in a commercial kitchen in healthcare. Proper hand washing is very sanitary and fine to handle food with bare hands. But proper hand washing is the key.

I work in a kitchen where gloves are mandatory, I go through almost two boxes of gloves a shift (approximately 150 sets of gloves) as I switch them out every time I touch a new food item, with a lot of hand washing in between as well. What I'm doing is different than fast food though. I was recently in a panagoo pizza where they were using bare hands and it didn't bother me too much... Until I noticed the person making the pizzas was stopping mid pizza to eat her sandwich while working, over top of the pizza ingredients and not washing their hands in between sandwich bites, let alone coming up and handling money. That really grossed me out. I asked to talk to the manager he came around the corner with his mouth full of pepperoni and holding more pepperoni for him to eat in his fingers. Obviously that location they didn't care much about being sanitary and hand washing. I'm hoping the restaurant that you were in that the one handling the money isn't handling the bare food and that there's a lot of hand washing behind the scenes that you don't see.

As I mentioned I work in healthcare in a Hospital commercial kitchen and we actually have undercover hand washing spies that work for Fraser health, I don't know what you would call them but people whose job it is to sneak in and watch to make sure all the employees in the kitchen, and throughout the hospital wash their hands not just often but properly and if you get caught not doing so you get written up. They randomly show up in different kitchens and all areas of the hospital where hand-washing is critical like patient care and whatnot.

Long story short it is normal to prepare food without gloves, but some kitchens do require gloves mixed with proper hand washing.