Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Upon the Qur’an’s permission and according to many scholars, Muslims are allowed to eat the foods of Jew and Christians (ahl al-kitab) regardless of what is recited on it, as long as it is not impermissible in Islam.
Responding to you question, Dr. Mohammad Qatanani, Professor in the Islamic American University and Imam of the Islamic Centre of Passaic County in New Jersey, states:
It is permitted to eat the food of the people of the scripture (ahlul-kitab). Allah Almighty says: “This day are (all) good things made lawful for you. The food of those who have received the Scripture is lawful for you, and your food is lawful for them.” (Al-Ma’idah 5:5)
The verse clearly allows Muslims to eat the food of the people of the scripture, i.e. the Jews and Christians regardless of any prayers recited on it.
Allah knows at the time of the revelation of the Qur’an that the People of the Book used to read their prayers to bless the food.
Many scholars like `Ataa’, Makhul, Al-Hasan, Ash-Sha`bi, Sa`id ibn Al-Musayyab, Al-Awza`i and Al-Layth all gave permission to eat animals slaughtered by Christians even if the name of Al-Maseeh “Jesus” is mentioned on it.
This viewpoint is in opposed by other scholars’ opinions who did not allow it.
With regard to non-slaughtered foods such as vegetables, there is no disagreement over its permissibility. However, you should mention the Name of Allah when you eat any food.
Allah Almighty knows best.