There is a misconception with regard to Muslims eating the food of Ahl-al-Kitab, that is the Jews and the Christians. It is believed by some Muslims that eating their food or meat is Haram because some of them associate partners with Allah.
However, in answer to that Allah came with an injunction in the Qur’an, chapter 5 verse 5. Allah says: “This day are (all) things good and pure made lawful unto you. The food of the People of the Book is lawful unto you. And yours is lawful unto them…”
From this injunction, Allah did not prohibit Muslims from eating the food of the Jews and the Christians. According to Yusuf Al-Qaradawi in his Halal wal-Haram Fil Islam (The Lawful and the Prohibited in Islam), the application of the phrase “the food of those who were given the scripture” is general and includes their meats, produce and other food, excepting what is haram in itself, eg. the flesh of a dead animal, pork, and blood.
Differences among jurists exist on the question of the lawfulness of consuming meat of the People of the Book slaughtered via crueller methods (eg. electrocution, decapitation, etc) or that which is speculated to have been slaughtered in the name of anyone other than Allah, or slaughtered by a non-Jew or non-Christian.
While some contend that such meat is haram, several conclude otherwise. Al-Tabari reported someone asking Abu al-Darda whether he could eat the flesh of a lamb slaughtered for the Church of St.
George that he had been given. Abu al-Darda responded in the affirmative, saying “O Allah, may You pardon us. Are they not the People of the Book, whose food is halal for us and ours for them?”
Imam Malik, when asked about animals slaughtered for Christian festivals, replied:
“I classify it as makruh but not haram; makruh because I am afraid it may have been dedicated to someone other than Allah but not haram because perhaps with respect to the People of the Book the meaning of the phrase ‘that which has been dedicated to any other than Allah’ applies only to those animals which they slaughter for the purpose of seeking the pleasure of their deities and not to eat. As for what they slaughter to eat, it is their food, and Allah says ‘The food of those who were given the Scripture is permitted to you'”
The famous Qadi Ibn al-Arabi further supports this permissibility for what is slaughtered by People of the Book as food. Responding to an enquiry about the lawfulness of partaking in the meal of a Christian who beheaded a chicken to cook it, he says:
“Eat it as this is his food and the food of his priests and monks. Although this is not our way of slaughtering the animal, Allah has permitted their food to us unconditionally and also other things in their religion excepting those which Allah says they have falsified. Our scholars have said they give us their women in marriage and it is permissible to engage in sexual intercourse with them. In matters concerning halal and haram, sexual intercourse is of graver import than eating; how then does it make any sense to say that their food is not halal?”
On another occasion, he declared “What they eat without intending to make it lawful for eating, as for example by strangling the animal or smashing its head, is haram.” (Both citations may be found in Qaradawi’s work mentioned above).
In the case of doubt as to how the animal was slaughtered, Imam Malik narrates a revealing incident occurring in the Madinan period of one who came to the Prophet (p) saying, “O Messenger of Allah, people from the desert bring us meat and we do not know whether they have mentioned Allah’s name over it.” The Prophet (p) replied “Mention the name of Allah over it and then eat it.” (Bidayatul Mujtahid, Vol.1, Book 14, Ch.4).