Is it even possible to have gluten in vodka? Vodka, by definition, alcohol and water. How the hell would gluten get in there in the first place?
I suppose, if it was made from wheat some trace might remain.
See this:
"*Unless gluten is added after distillation, all distilled alcohols are gluten-free. However, US labeling laws prohibit beverages that use cereal grains at any point in the manufacturing process from advertising themselves as ‘gluten-free.’
Many people with celiac disease choose to avoid distilled beverages that use cereal grains in the m*anufacturing process, while many others drink them with no adverse effects."
It’s mostly a advertising thing, Titos is made from corn, which is also cheap.
Of course Vodka shoudl be made from potatoes,
which would also be “gluten free”.
If it is made with wheat, the association is that there will be gluten involved. Maybe look for a potato based vodka to appease those people.
On the other hand, it may just be marketing mumbo jumbo. Like whole grain popcorn or something.
Many people know that “gluten is bad” or that “people with coeliac disease can’t eat gluten” without knowing what the heck it is, or how it gets into food in the first place. That the word happens to mean two very different things in a biochemical(1) and an alimentary(2) context doesn’t help. My current client uses maize as their only biological raw material, but they’ve got the “gluten-free”, “kosher” and “halal” labels. In theory they could label their maize gluten as being gluten-free! (They don’t). It simply makes marketing sense to get the labels if you can.
1: any protein naturally found in a cereal. In this context, maize and rice have gluten.
2: those proteins, mainly from four specific cereals (wheat, rye, barley and oats), which happen to trigger symptoms in people with coeliac disease. In this context, maize and rice do not have gluten; it’s not that their proteins have magically disappeared, but they don’t cause problems to people with C.D.
But of course Gluten **isn’t **bad. Unless you have a couple of rather rare medical conditions.
I personally know one woman who decided she was allergic to gluten, and after a month on a Gluten free diet was telling us how much better she felt and that she had lost weight.
As I pointed out- sure, since she used to eat lots of white bread, cookies , doughnuts, cupcakes, etc, cutting the junk food out would make her feel better and lose weight.
My wife is a celiac’s* and while most wheat-distilled vodka is supposed to be gluten free, she’s gotten a reaction** before from beverages that contain those types of vodka. Now, we mostly stick to potato-based vodkas. Or no vodka at all (she’s a huge rum drinker now).
It’s only ancedata but take it for what it’s worth 
- Long story short, she’s not technically officially diagnosed as celiacs, just as gluten-intolerant. But that’s because the celiac’s blood test requires you to be actively ingesting gluten for it to turn up positive for the antibodies and she was on a GF diet for a few months before the test. But since she was feeling much better and not getting the symptoms she’s stayed off. Her doc now thinks she’s probably full-blown celiacs because of a related autoimmune disease she’s been officially diagnosed with.
** Mouth sores, mostly. Though lots of gluten would cause her to have stomach issues and get what she calls “foggy brain”. Also joint pain. But the vodka one was based on mouth sores.
Have her try some aged rum. You can sip it, just like single-malt.
Check her toothpaste for SLS, sodium lauryl sulfate and variants. Often causes mouth sores and has no dental benefit.
Smirnoff is gluten free (corn).