Locally-slaughtered meat in a country with a mixed population of Muslims, Christians and idol-worshippers

If the matter is as described, with the meat being slaughtered by a mixture of people that includes people of the Book, idol-worshippers and ignorant Muslims, and you cannot tell who has slaughtered what and it is not known whether the name of Allaah was mentioned at the time of slaughter or not, then it is haraam to eat the meat when you are confused about who did the slaughtering, because the basic principle is that animals of the an’aam class (i.e., camels, cattle, sheep and goats), and animals that come under the same rulings, are haraam unless they are slaughtered in the proper manner as prescribed in sharee’ah. In this case there is doubt as to whether the slaughtering is done in the proper shar’i manner or not, because of the mixture of slaughterers, some of whose meat is permissible and some is not permissible – such as the idol-worshippers and innovators among the ignorant Muslims whose bid’ah involves shirk. 

If it can be determined what has been slaughtered by whom, then you can eat meat slaughtered by a Muslim or a Christian if it is known that he mentioned the name of Allaah at the time of slaughter, or if it is not known whether he mentioned the name of Allaah or not. But you may not eat meat slaughtered by an idol-worshipper or by a Muslim who follows innovation that involves shirk, whether he mentioned the name of Allaah over it or not. 

The Muslim should strive to be on the safe side in all matters of religion and he should seek that which is halaal in his food, drink, clothing and all his affairs. With regard to matters such as that asked about here, the Ahl al-Sunnah should choose the right people to slaughter their meat.