If someone reacts to gluten, are foods allowed with “May contain traces of gluten“ written on the package?

If someone reacts to gluten, are foods allowed with “May contain traces of gluten“ written on the package?

There is little likelihood that the products actually contain gluten. This expression means that the product was produced in an environment where also gluten containing foods are processed. So if you don´t have celiac disease you are free to enjoy them.