I keep my ketchup in the fridge... But, if you think about it, restaurants don't refrigerate ketchup, even after it's been opened... Some people claim that you don't need to refrigerate mayo either. Once it's been refrigerated, it will go bad if left out, but according to them, if you never refrigerate it, you never need to. They eat it without getting sick, so maybe they're right.
I refrigerate everything, just cuz I'm weird I suppose. On the other hand, what drives me bananas is that my inlaws leave pitchers of milk ON THE COUNTER ALL DAY and can't figure out why their milk goes bad.
I checked the Hunts bottle and I do not see "refridge after opening" on it. Good luck on not keeping the mayo in the fridge!!!