Background to The Kosher Status Of Cheese Milk from a Kosher beast is Kosher. Milk from non-Kosher beasts is not Kosher.
The Torah permits us to use milk from a non-Jewish farmer even though there is a risk that the farmer may include some milk of non-Kosher beasts in his milking. I will not explain this by going through the various Halachic arguments but by observing that the Rabbis made a decree to prohibit such milk. Clearly, if the Rabbis promulgated a decree to ban it, it must be Kosher by the Torah’s standards.
Yet, even after the decree forbidding milk sourced from a Gentile was in place, we were nevertheless permitted to eat cheese manufactured by a Gentile (RaMBaM MaA’ChoLos A’SuRos 3:12, 13 & 14). Although cheese is made from the same milk collected by the non-J farmer and one would expect that it would be equally banned under the Rabbis’ decree, this is not the case. The reason for this, explained in the Gemara, is that cheese can not be made from the milk of non-kosher animals. Therefore, the gentile cheese manufacturer will not waste his time and his milk in a useless exercise. So we can safely assume that the milk collected for cheese-making will be pure cow, sheep or goat milk, which is Kosher.
There is a second consideration that covers the cases where some non-kosher milk was included in the milk processed into cheese. This may happen when milk is initially collected for the purposes of being used as a liquid and is later re-assigned to be used for cheese production. Even this case poses no Kashrus concerns since the cheese-making process is actually a filtering process. All the non-K milk will drain away from the curds that form from the milk and which are converted into cheese. Thus the final product is free of all traces of non-K milk that may have been or were in the milk.
But There is More To Cheese Than Milk Now the milk is not the only component that may render the cheese not kosher. Rennet, a family of enzymes produced by the calf’s fourth stomach, is traditionally used (these days artificial, microbial rennet substitutes are available) to convert milk into cheese. How were we ever permitted to eat cheese made by our non-J neighbour, which certainly contained rennet from a non slaughtered animal? We can not argue that the rennet is present in only insignificant proportions and therefore of no consequence since its effects are profound and pronounced; it is a DaVar HaMaAmid.
Things That Are Not Foods The explanation is that enzymes are not foods (RamBaM MaA’ChoLos A’SuRos; 4:19) and therefore although they are produced by and extracted from a non-kosher animal they are kosher or more accurately, they can not be non-Kosher since they are not food. This is true notwithstanding the fact that the enzymes are expressly harvested and used for processing foods.
Nectar Is Not Honey Until It Is Modified The same can be observed from honey, which the Gemara (BeChoRos 7b) explains is kosher since it is not actually produced by the bee but is simply nectar that has been collected and modified by the insect. Of course this modification occurs through the enzymes produced by the insect. Again, since the enzyme’s effects are profound and pronounced, they can not be considered insignificant and deemed of no consequence. Honey is thus kosher in spite of its being a profoundly altered food through the enzymes produced by a non-kosher insect.
Of course the truth is that enzymes are kosher because they are not a food, and can be and were used for Kosher cheese-making. Consequently, cheese produced by Gentiles was Kosher.
The Nature and Purpose of Rabbinic Decrees Even following the Rabbis' decree requiring that milk be supervised to be Kosher, cheese manufactured from unsupervised milk was Kosher.
Keep in mind, the Rabbis were mainly driven to promote habits that would maintain the community's integrity and prevent assimilation. They were attempting to construct barriers that were unpopular. Disallowing various foods was a very successful strategy but it required persuading the community that it was for a legitimate reason - to remain faithful to the laws of Kashrus. So, the milk decree was embraced since it offered the assurance that it was pure and not adulterated with milk from non-Kosher animals, even though by Torah Law the milk is Kosher without such assurances.
Cheese however was not banned, even when made from unsupervised non-Kosher milk, because everyone was aware that cheese is only made from the milk of Kosher animals. So although we had to supervise the milking in order to buy a pint of the non-Jew's milk, we could buy a pound of his cheese.
However, the opportunity to ban cheese from non-Jews soon came. Probably for reasons of convenience, they stopped using the contents of the stomach to make cheese, rather using the flesh of the stomach itself, which contained the glands that produced the rennet. It was either left to soak in and then removed from the vat of milk; or it was dehydrated (giving it a prolonged shelf life) and pulverised, the powder being added to batches of milk.
Now the Rabbis had a persuasive argument to ban cheese manufactured by non-Jews. Since it was not just the enzyme being added but also the flesh of the stomach which is a food.
This ban included all cheeses, even those made without animal rennet and according to many requires not just supervision but actual participation in the manufacturing process.