Are vodka, beer or other alcoholic beverages commonly distilled with genetically modified ingredients?

Beer isn't distilled at all, but any alcoholic beverage made with wheat or corn is made with genetically modified grain. They were not modified with gene splicing and that, but they were bred and cross pollinated with the intent of increasing yield and other properties. Beer is made mostly with barley. I don't know how much genetic engineering has been done with barley.