Shaykh Salih al-Fawzan states that eating the meat of Jews and Christians is generally permissible because they are People of the Book. However, if it is known that they do not slaughter according to Islamic rules, then their meat becomes impermissible, just like a Muslim who does not follow proper slaughter.
May Allah be good to you O’ respected father. What is the Islamic ruling on eating meat from foreign lands that follow Christianity?
There is no problem (in eating) the sacrifices of the Jews and Christians. (Allah ﷻ says)
۞وَطَعَامُ الَّذِينَ أُوتُوا الْكِتَابَ حِلٌّ لَّكُمْ وَطَعَامُكُمْ حِلٌّ لَّهُمْ
“..and the food of the people of the scriptures is lawful to you.” (Q 5:5).
Their food (referred to here) is their sacrifices. It is permissible (to eat) by consensus. However, if it is known that they do not slaughter in accordance to Islamic legislation then it is not permissible (to eat their meat). Just like a Muslim, if he does not slaughter in accordance to the Islamic legislation , then his slaughtering is not permissible. So how about with regards to a disbeliever?