I think the first thing we need to ask before digging into this question is whether or not gluten can become airborne.
When thinking about baking or using any particle type substance containing gluten; the first thing I think of is getting flour everywhere. Hand prints on my pants, in my hair and all over the bench. With that in mind it should be easy to answer that question. Yes it is physically possible for gluten to become airborne.
So now down to the real question. Is it possible that airborne gluten will contaminate me.
When the flour particles are flying around in the air and landing on bench space and utensils; of course you are also inhaling them. You might not think that inhaling gluten particles is such a big deal however your nose and mouth are all connected and if you breath in the particles through your nose they can be transferred through your mucus into your digestive tract.
When considering this in respect to food preparation in a non gluten free environment airborne contamination is a real threat and it can do damage to your intestines. However, airborne gluten is more of a threat, in any restaurant that uses dry flour in their cooking area. Pizzerias, Italian restaurants that make fresh pasta and any other cuisine that employs the use of dry flour during preparation should be avoided entirely. This includes bakeries that do not have a separate preparation and cooking area for their gluten free products.
Although restaurants that do not use dry flour or other particle type gluten products in cooking or preparation are considered safer they still possess the potential to contaminate you. So always eat out at your own discretion.
Shared ovens and microwaves should also be avoided as food tends to splatter around the edges and can contaminate your gluten free food unless properly washed.