Does apple cider vinegar need to be refrigderated?
No. Absolutely not.
I don't refrigerate mine and it's fine.
First place to check for information is the label on the bottle. Unless it says "refrigerate after opening" you wouldn't have to. Vinegar is already/supposed to be spoiled, sour, fermented, so it won't go bad under normal conditions.
This begs a question - do any vinegars need to be refrigerated? I usually have white and red wine, sherry, rice wine, cider, balsamic and sometimes champagne or malt vinegars on hand - and it's never occurred to me to store them in the fridge.
I know the labels don't say to do it, but some things keep better refrigerated (e.g., nuts) even though not usually labelled that way. Vinegar?
Vinegar is a preservative so it doesn't need to be preserved by refrigeration.