Personally, I refrigerate anything that says Refrigerate after opening. Even if it’s preceded by For best results. Ketchup falls into that category.

The best before date is based on it being refrigerated and the reason why we do it is to slow bacteria multiplication to a crawl

I like the temperature contrast between cold ketchup and hot food so mine is in the fridge.

non refrigerated ketchup always tastes funky unless it’s the kind that’s packed with a large enough buttload of preservatives that they no longer have to put “refrigerate after opening” on the bottle.

Ketchup belongs in the fridge, to cut the heat. Otherwise it’s too spicy.