They have GF empanadas in a separate case. I think they use the same oven to warm them but seems to be limited contamination and decent options.
This is the only place I've found in the city to offer gluten free empanadas! They keep them in a separate case from the rest and offer a more limited selection, but I really like the ones they have, and I've never come when they didn't have any. They even have some cheese-free ones, which is great for me because I also have a dairy allergy. If you don't have a dairy allergy, I think you can also have their gluten-free alfajores (made of corn flour). They also offer tasty salads and drinks in the fridge that have every ingredient printed on them. The seating is a bit hole in the wall, but cozy. Love this place!!