I basically just go by whether or not it was refrigerated in the supermarket. However, once it's opened I mostly throw everything in there except for dry stuff.
Good general rule. Only exception I can think of is there are a few fruits they'll refrigerate in the back and then often display at room temp, since a few hours at room temp doesn't hurt them much. Apples, oranges, stuff like that.
It's pretty common actually. There is a large walk-in cooler in the back where perishable backstock is stored. When new apples are needed, a big box is fetched from the cooler and the apples are restocked in the display.
Most of the stuff is kept in the back cooler, only things left out are those harmed by refrigeration like tomatoes or those that don't go bad for a long time.
With apples it extends their life by quite a long time though. Probably over double.
products with any sort of packaging also say how they should be stores pre and post-opening, e.g. canned goods are generally fine to keep in a cupboard until opened where they then need to be in the fridge.