Updating this old thread with some new information:
First of all, I have learned that vinegar is made commercially in a two stage process that begins by fermenting and then distilling alcohol, then in a second process bacteria are used to break down the alcohol into acetic acid. Finally the resulting highly acidic mix is diluted, typically to 5% acid. Vinegar is, after all, acetic acid.
I found a very detailed explanation of the
process used to create distilled vinegar, the author, a retired professor of biochemistry with celiac disease, concludes that a person could drink up to 100 liters of distilled vinegar per day without exceeding the minimum level of gluten exposure considered safe in Europe. Obviously nobody is going to drink one liter of vinegar, let alone 100.
However there is one type of vinegar that all people with celiac disease should definitely avoid at all costs, that is malt vinegar.
In the US we do not often see malt vinegar used as an ingredient in prepared foods, but in the UK it is widely used and can be found in virtually every chip shop (where fish and chips are sold). Malt vinegar is made with barley malt, and some barley malt mash is present in the final product as flavoring. It is wise to consider malt vinegar as always containing gluten, avoid it like the plague.
Apple cider vinegar, wine vinegar and rice vinegar are the 3 forms most used in home cooking, at least in my experience in the USA, and these can be expected to be gluten free because apples, grapes and rice are gluten free.
I reiterate that the warnings against use of distilled vinegar by people with celiac disease are a persistent myth with no basis in reality. There are some people who report experiencing abdominal discomfort after eating foods containing distilled vinegar. I do not know why this happens, but since there is no detectable level of gluten in distilled vinegar it is not caused by a gluten reaction to gluten in distilled vinegar.