Is there residual alcohol in various vinegars?
Yes, there is some alcohol in vinegar.
Estimates of Ethanol Exposure in Children from Food not Labeled as Alcohol-Containing, Gorgus et al., Journal of Analytical Toxicology 2016  discusses a range of sources of alcohol exposure, some of which might be surprising.
Among them is white wine vinegar, which is quoted as having 2.6 g/l.  That's around 0.25% ABV (vinegar is mostly water, and acetic acid has a similar density to water, so close enough). I can see no reason for other real (brewed) vinegar to have appreciably less. Consuming a unit/standard drink of alcohol would mean drinking large quantities of pure vinegar (a UK unit is 8 g of pure ethanol, so that would mean drinking about 3 litres of vinegar), so for the majority of people this wouldn't be an issue; indeed the human body produces several grams per day (Wikipedia link, but see the cited source for this claim for a full review).
However if someone is trying to completely avoid consuming any alcohol, vinegar would seem to be off limits.  There are alternatives, such as &quot;non-brewed condiment&quot; a malt vinegar substitute made from industrially produced acetic acid, water, and flavours. Similar products may legally be allowed to be sold as vinegar in some countries - they should be cheap, and include &quot;acetic acid&quot; on the list of ingredients (see Wikipedia's article for links to other languages).
It appears to be possible for consumers to buy food-grade acetic acid at high concentrations. This would need to be diluted significantly. One brand I found was described as 70% acetic acid; as common vinegar is no more than about 5%, you'd need something like 1 part of that 70% product to 12 parts water (or fruit juice, or a mixture of the two) and undiluted it should be handled as a nasty chemical rather than as a food (protect eyes and skin, avoid inhaling fumes).
Industrial production is done directly, without the alcohol intermediate step, so can be assumed to be alcohol-free and would also allow some distance from the alcohol industry, if that's related to the motivation.
Returning to the paper I linked at the start, some other foods may be  surprisingly high in alcohol.  Some breads, for example have over 1% by weight (though others have no detectable alcohol).  Very ripe fruit has some, and fruit juices contain tiny quantities, with the highest figure detected in the juices around 1/3 of that in vinegar, at less than 0.1%, though of course fruit juices are often consumed in larger quantities than vinegar.  Perhaps the natural level found in fruit juices could be regarded as a practical threshold to consider functionally zero, barring any medical reason to go still further.