Depending on the PH levels they may never “go bad” as in, suffer bacterial or fungal growth. (Anything lower than about 4.6ph will have much lower chances of spoiling but this risk is not eliminated completely and there are plenty of people who get botulism poisoning from high acidity foods improperly stored, this is because while the bacteria may not thrive there, their highly toxic bi-products may persist even through cooking.)

But that’s not the only reason we refrigerate stuff. Food, including condiments that are salty or pickled, are made of organic molecules, oftentimes many different kinds of complex molecules. These delicate structures begin breaking down the moment they’re created the same way a jiggling lego tower will eventually become unrecognizable.

Refrigeration slows this jiggling and preserves the structure of these molecules, preserving the flavor and nutrition much longer than if you leave it out. If you go through those condiments fast, in less than a couple months, it should be fine, but everything eventually reaches a point where it doesn’t have the same flavor or texture anymore and it won’t be as nice as fresh ingredients.