2022 update:
Handling of gluten free ingredients has improved: the gluten free bread stays packed until it is prepared in a dedicated kitchen space. Separate tools and cutlery are being used to prepare it. Waiting staff is very knowledgeable on allergens & kitchen routines.
2020:
They offer gluten free bread & buns upon request, however do not have a dedicated space to prepare it. Cross-contamination therefore is present at all times.
Okey if avoiding gluten for taste however not suitable for sever sufferers.
The only gluten-free option on their breakfast menu is the vegan „Del Prado“ set brekkie.
It is a generous portion of high quality ingredients that are naturally gluten free. Gluten free bread is served upon request.
Still, beware that food is prepared in the same area as gluten containing foods.
Most of the items contain dairy products as well (e.g scrambled eggs). For the set breakfast options (called „Stadtbekannt“) one can swap single ingredients, for instance butter for vegan butter/another spread, as long as the swap equals the price range of the original ingredient.
Find their menu here (English version at the end)
http://www.kunsthauscafe.co.at/download/Speisekarte_Web.pdf?cache=none
— Somewhat
— Gluten-free items are marked on the main menu
— Not Much
— Good
Very nice Gluten free burgers
— Gluten-free items are marked on the main menu
— Some
— Excellent