Commentary for Avodah Zarah 58:4

The concern with regards to fish brine is that there may be small amounts of wine in it. Bithynian cheese is cheese that comes from a place called Bithynia, which is in Asia Minor. According to the Talmud most of the calves raised there were used for idol worship. Since cheese uses rennet, a substance which comes from the stomach lining of a cow and solidifies the milk into cheese, we are concerned that the rennet came from a cow used in idol worship. Due to our concern with both of these foods, Rabbi Meir says it is forbidden for a Jew to derive benefit from either. According the Sages it is only forbidden to eat them; it is permitted to derive benefit from them. The fish brine is permitted since the wine was only used as an antidote for any polluting agent in the brine and not for its own taste. The cheese is permitted since most of the animals in Bithynia were not used for idol worship, only most of the calves which were a minority of the total number of animals.