Finding your way around
Does "gluten free pizza" set off a gluten warning?
No.
No. The alarm reads what you wrote, including the negatives: gluten free, dairy free, no nuts, without egg and non-dairy all mean the thing is not there. It still warns you if you name the thing again somewhere else, so "gluten free pizza and a side of gluten crackers" is still flagged. It reads what you wrote and does not work out what is in a dish, so name anything you need us to see.