Praise be to Allaah.
Before answering this question, it is important to know what rennet is.
Al-Fayroozabaadi said in al-Qaamoos al-Muheet (p. 313), under the definition of na fa ha: al-infahah and al-minfahah and al-binfahah all refer to something yellow that is extracted from the stomachs of suckling goat kids.
Infahah (rennet) was also defined in al-Mawsoo'ah al-Fiqhiyyah as follows: "It is a yellowish-white substance ([in a skin vessel] - this phrase appears not to fit here) that is extracted from the stomachs of suckling kids or lambs. When a little of this substance is added to milk, it curdles and becomes cheese. In some Arabic-speaking regions, people call this rennet mujabbinah (cheese-maker), and the stomach (from which the rennet is taken) is called kursh if the animal grazes on grass.
The Islamic ruling concerning rennet is that if it is taken from an animal that has been slaughtered according to sharee'ah, then it is pure (taahir) and can be eaten. This is according to the Hanafis, Maalikis, Shaafa'is and Hanbalis.
As regards eating rennet taken from an animal that dies naturally, or that was not slaughtered in accordance with sharee'ah, according to the apparent meaning of the opinions reported from the majority of scholars among the Maalikis, Shaafa'is and Hanbalis have said, it is impure (naajis) and should not be eaten. They base this ruling on the aayah (interpretation of the meaning): "Forbidden to you for food) are: al-maytatah (dead animals - cattle-beast not slaughtered)…" [al-Maa;idah 5:3] - the rennet becomes impure by virtue of the animal's death, and it is not possible to remove that impurity from it. [next phrase is unclear]
Imaam al-Nawawi said in al-Majmoo' (9/68): "The ummah is agreed that it is permissible to eat cheese so long as it is not mixed with anything impure, such as adding rennet from a source that is not halaal because it was not slaughtered according to sharee'ah. This ijmaa' (scholarly consensus) is the evidence for its permissibility."
The second view, which is that of Abu Haneefah and is one of two opinions narrated from Imaam Ahmad, is that rennet from dead animals or animals that were not slaughtered according to sharee'ah is still taahir (pure). This is the opinion which Shaykh al-Islam Ibn Taymiyyah thought most correct in al-Fataawaa (21/102), where he said: "It is more likely that their (the Zoroastrians') cheese is halaal, and that the rennet and milk of dead animals is taahir (pure)." Elsewhere in al-Fataawaa (35/154) he said: "With regard to the cheese made with their (some of the kaafir Baatini groups') rennet, there are two well-known scholarly opinions, as is the case with the rennet from animals slaughtered by the Zoroastrians and Christians, and rennet from dead animals, of whom it is said that they do not slaughter their animals properly. The schools of Abu Haneefah and Ahmad, according to the other of his two opinions, say that this cheese is halaal, because the rennet taken from dead animals is taahir (pure), according to this view, and because the (enzymes in) rennet do not die when the animal dies (so, the concept "impure containers don't cause the contents of the container to become impure by contact" ) applies. The schools of Maalik, al-Shaafa'i and Ahmad, according to the other of his two opinions, state that this cheese is naajis (impure), because the rennet is impure according to this view, as they see the milk and rennet of dead animals as impure. In cases where meat is classified as impure because it is not slaughtered properly, the meat is regarded as being the same as dead meat. Both opinions are based on reports narrated from the Sahaabah. The first group states that the Sahaabah used to eat the cheese of the Zoroastrians, while the second group state that the Sahaabah used to eat what they thought was the cheese of the Christians. With regard to this issue, the follower (ordinary Muslim) must follow an 'aalim who advises him to follow either of these two opinions.
Sheikh Muhammed Salih Al-Munajjid