All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
All the scholars are agreed on the lawfulness of eating cheese made from calf rennet if that calf or animal is slaughtered according to Islamic rites. However, they differed in opinion in regard to the rennet of an animal that is not slaughtered according to Islamic rites. Some of them are of the view that it is lawful to eat it basing their argument on some reports that the companions ate cheese made by the Magi and which was mixed with the rennet of animals which were dead animals (i.e. not slaughtered according to Islamic rites). Other scholars, however, are of the view that it is forbidden because what is taken from a dead animal is itself a dead animal (dead meat). Therefore, we advise you to act according to the better opinion as much as possible in order to be on the safe side and avoid the difference of opinion. If you can not do so, then you should only take according to your need [necessity]. Indeed, the difference of opinion among the scholars is a mercy in such issues.
As for what is taken from a live animal, all the scholars agree that it is lawful because it is taken as a liquid that has nothing to do with the body of the animal it was taken from.
Its ruling is the same as the ruling of vomits of an animal that we are allowed to eat, and this is pure according to the agreement of the scholars, like its saliva and spittle.
Note: Animals slaughtered by Buddhists are like animals slaughtered by the Magi since they are not from the People of the Book. So, they are considered Meytah (animals not slaughtered according to the Sharee'ah). This is the ruling concerning cheese. As regards butter and fat, they are permissible even if they are made by the Magi or Buddhists. But if they add any impure thing to them, then they (i.e. butter and fat) become unlawful.
Allah knows best.