In Shulchan Aruch Yoreh Deah Siman 97 it says that it's ossur to bake "milchig bread" -- lest you come to eat it with meat (although if it's made in a small amount or with a change in it's look from normal bread than it's muter.) Such bread if made in a way that's ossur, would be ossur to eat even by itself.
However what about the celim that the bread was baked in? Would those celim be "ossur" now just like the bread is?
We find in Yoreh Deah Siman 113 that the celim that a non-Jew cooked food in would need to be kashered. While there is a maklokes Rishonim about this and the Shulachan Aruch brings down 2 opinions it seems that the accepted psak l'maseh is that the celim need to be kashered. The reason being is that since Chazal were gozer that the food is ossur, then just like any other issur, the blias also become ossur (granted though there are Rishonim that argue and the Gra over there says that the reason of the issur of bishul akum wouldn't be shayach by blias.) However if we accept the machmirim by bishul akum that since the food become ossur, so to the blias, would the same be true by milchig bread? If not what's the proof or reasoning that the celim should be permitted?
