As a former competitive brewer, let me give you the straight scoop. When extracting the sugars (which will be fermented later) from barley and wheat, a "lauter tun" is used. It creates a bed of cracked grains which have gone through a precise series of temperature steps to break down the starches by enzymes which are present in the grain (amylase A, Amylase B, as well at protease to break the complex protean molecules into simpler peptides). You let the bed rest a short period, which allows the gluten to "set". The bed creates a filter which helps reduce amount of unreduced grain from entering the liquid which will be fermented for beer. The presence of gluten or starch causes an undesirable haze in the beer. Most brewery facilities try to keep these undesirable substances out of their beer. Good clear beer is gluten free. Whiskey is a distilled product of a "beer-like" liquid (typically without hops). As such, it is also gluten free. Nobody would like or appreciate a "cloudy" whiskey.
If the drink is clear, don't sweat the gluten.