Gluten proteins won't make it into the distilled product.
Some grains (spelt, wheat) are high in gluten whereas others (barley, rye, oats) are low to very low in gluten content but spirit made from any of these sources are totally gluten free regardless.
I do know that a couple of amateur celiac groups out there say to avoid grain based spirits, but it's just words.
bhomstead wrote: or are we living by assumption and legend, that there is no gluten in distilled beverages.
I would have to answer 'yes'.