My wife is dairy free, and I am gluten free! How difficult are Irish restaurants and taverns to customers with food allergies?
I'm finding in much of Europe, they are aware of allergies and can let you know what is safe to eat. Some menus even let you know. The two you have are very common.
EU food labeling rules are pretty strict. As far as I can remember all menus list common allergens. I distinctly remember seeing notations regarding gluten. I don't recall notations regarding dairy. Maybe someone else's memory is better. And you can always ask.
All menus are required by law to list allergens including gluten and dairy.