Sheikh `Abd al-Wahhâb al-Turayrî, former professor at al-Imâm University in Riyadh
Animals slaughtered by Christians and Jews are lawful for Muslims to eat. This is not contingent on their firmness on their religion, because the the Jews and Christians who lived in the time of our Prophet’s (peace be upon him) had already altered their teachings and deviated from their religion. In spite of this, Allah says: “The food of the People of the Book is lawful unto you and yours is lawful unto them” [Sûrah al-Mâ’idah: 5]
Therefore, the meat they sell in their supermarkets and restaurants is lawful, provided they slaughter their meat properly, and do not use alternative methods like electrocution or suffocation to kill the animal.
And Allah knows best.
Source: Islam Today