The sauce of many disagreements...

Is that that stuff Aussies squirt on meat pies that the rest of us call ketchup?

Depends where you buy it.
If you buy it from a chilled section, chill it. If you buy it a room temp. keep it at room temp.
Still baffles me why some folk put fruit; veg and even eggs in the refrigerator.
Hardly their best environment i would have thought.

I put it in the fridge

Never in the fridge.

I'd put it in the fridge if I can't use it in one go but until it's opened it can stay out

It can usually sit on the counter because of the preservatives but better in the ice box.

after its been opened we keep it in the fridge

Pantry until opened

No to cold condiments

Hmm surely that should be a picture of me