Soy, vinegar, Worcester sauce don’t need refrigeration.
There are oils that go off quickly and the process is slowed by keeping them in a cool dark place. (long chain fatty acids are sort of my thing…)
Ketchup is usually pretty safe, but that icky stuff that builds up around and dried at the top should be wiped away. My kid likes cold ketchup, so we keep it in the fridge.
Generally, if it has a high percentage of water and sugar (and many do) it will grow microbes. Bacteria will grow in the water and sugars make yeasts and other molds very happy. When there is enough vinegar and salt, the pH will protect the solution from growing the most harmful of the nastiness.
As far as mayo goes, I’d be careful. Follow what the brand says on the container. They have different amounts of salt, sugar and liquid but are made from raw egg. I would read what is recommended on the jar or bottle. You also need to remember that mayo is made from different types of oil and depending on the freshness of that oil, it can oxidize quickly. It is better to keep real mayo in a cool dark place, like your fridge, but leaving it out overnight once won’t kill it. I’m just saying that best practices to keep it good tasting, I keep my real mayo in the fridge.
Vinegar, soy sauce and alcohol are all made by fermentation. They do not need refrigeration, but some tastes are better served cold. I like my beer or white wine chilled, but my soy sauce and sake warm.