FYI I don't have GI symptoms, so I can't know if there was cross contamination, but there isn't a lot of information out there for Zagreb so I wanted to post my experience. The waitress spoke English. I also showed her my card that explained celiac disease in Croatian - she knew immediately what I was looking for and walked me through the menu to show me what was safe for me to have.
My sister is a vegetarian, and she also had a good experience.
Food was good. Staff were aware of gluten free and while not marked on menus they were able to identify what items were and weren’t gluten free including on the basis of cross contamination alone.