Avodah Zarah 36 - Milk, Bread, and Oil of Idolaters
Milk that an idol worshipper milked without a Jew seeing him is prohibited to drink, though not prohibited for benefit. Although the milk of a kosher animal is white, and that of a non-kosher animal is yellowish, if some amount of non-kosher milk is added to kosher milk, this will not be easily discernible.
Bread of an idol worshipper is forbidden because frequent consumption of it may lead to intermarriage. Technically, the bread is kosher, for we can assume that the flavors that it had absorbed are more than a day old, and thus do not make the bread forbidden. Therefore, the bread of commercial bakers, the consumption of which does not lead to socializing, should have been permitted. That is how many people had understood the prohibition, and this absence of complete acceptance by the majority formed the basis for later leniences.
The oil of idol worshippers was prohibited because using it too can lead to intermarriage. However, since it is a necessary staple, a later court annulled this prohibition.
Art: Adolphe Charles Marais - The Milkmaid