If it's in a sealed plastic bag it doesn't go stale until long after it would have molded on the counter. I refrigerate mine because I buy Costco sized sliced bread and it takes me 2 months to go through it. If you toast your bread, the staleness is unnoticeable

A lot of these things only need to be refrigerated to preserve flavor, not to stop spoilage. If you go through a bottle of ketchup in 3 months there is little benefit to refrigerating it, if it takes 3 years for you to finish it, it should probably stay in the fridge.

Some peanut butter brands require refrigeration to prevent mould. Others recommend it because it stops the oils from separating. Brands like Kraft don't require any refrigeration at all

Refrigerating oil will stop it from going rancid, but I've only ever needed to do this with used deep frier oil

Honey is just a hell no in the fridge