The basic principle is that meat slaughtered by Muslims and the People of the Book is permissible, unless it is proven that they mention something other than the name of Allah at the time of slaughter or that they slaughter the animal in a manner that is not acceptable according to shareeah.
The scholars of the Standing Committee said:
It is permissible to eat meat slaughtered by the People of the Book, the Jews and Christians, if they mention the name of Allah over it as well as fulfilling all the other conditions of slaughter as known in Islam. If they mention the name of anyone other than Allah over it, such as al-Uzayr or the Messiah, then it is not permissible to eat it. Similarly, if they kill it by strangulation or electric shock, it is not permissible to eat it.
End quote from Fataawa al-Lajnah ad-Daa'imah, 22/391-392
If it so happens that the People of the Book sell pork in the same shop where halaal meat is sold, the basic principle is that the place where the evil is committed should be shunned and its people should not be helped in that regard, but this does not mean that their meat that was slaughtered in the Islamically prescribed manner is haraam, or that interacting with them in general is haraam, especially when there is a need for that, and you will encounter difficulty if you stop buying from them, and there is no one else like them from whom you could buy things.
The scholars of the Standing Committee were asked:
Is it permissible for a Muslim to buy halaal meat from a store that also sells haraam meat, if each type of meat is in a separate location and is stored in a separate fridge, and the meat is packaged separately? Is it permissible to buy halaal kinds of food from a large store, if that store also sells alcohol in a separate section of the store, and the owner of these stores is not Muslim?
Allah, may He be exalted, says (interpretation of the meaning):
Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression
Hence it is not permissible for a Muslim to help anyone in anything that involves sin and transgression or in transgressing the sacred limits set by Allah. Therefore, if the Muslim has a choice, in that there are people who sell halaal things and refrain from selling haraam things, such as pork and so on, then he should deal with him, and not with the one who sells both halaal things and haraam things such as pork, alcohol and so on.
But if that is not possible, then it is permissible for the Muslim to buy halaal meat and permissible foods from him, so long as there is no confusion between the halaal meat and the harasm meat, because Allah, may He be exalted, says (interpretation of the meaning):
So keep your duty to Allah and fear Him as much as you can
End quote from Fataawa al-Lajnah ad-Daa'imah, 13/173
If these amulets that are hung up in the shop contain anything that constitutes shirk (associating others with Allah), such as asking of anyone other than Allah, seeking the help of the awliya' (close friends of Allah, sometimes called saints) and the like, or if you know that the owners of these shops are people who practice and promote these kinds of shirk, or they believe that these amulets that they hang up can, besides Allah, bring benefits or ward off harm, then the meat slaughtered by them is not permissible, because these things constitute major shirk.
But if these amulets are free of major shirk, and it is not known that these people wear them or believe that the amulets can bring benefits or ward off harm, then the meat slaughtered by them is permissible.
The fact that a person has fallen into minor shirk - but not major shirk - does not mean that it is not permissible to eat meat slaughtered by him.
The scholars of the Standing Committee were asked:
What is the ruling on meat slaughtered by a person who uses amulets containing words from the Qur'an or otherwise, or who ties knots with thread and so on?
They replied: Amulets are things such as pearls, sea-shells and so on that are put around the necks of children, animals, women and so on, or may also be tied to their belts or their hair, to protect against evil or to ward off harm. This is forbidden and in fact is shirk (associating others with Allah), because it is Allah alone in Whose hand is control of benefit and harm; no one else has this power.
Anyone who believes that an amulet and the like has any power to bring benefit or ward off harm is a mushrik in the sense of major shirk that puts him beyond the pale of Islam - Allah forbid - and meat slaughtered by him is not to be eaten.
Anyone who believes that it is just a means and that Allah is the One who brings benefits or causes harm, and that He is the one who brings about the effects of causes is a mushrik in the sense of minor shirk, because an amulet is not a regular means and it is not prescribed in Islam; rather it is just something imaginary.
End quote from Fataawa al-Lajnah ad-Daa'imah, 22/433-434
Shaykh Ibn Baaz (may Allah have mercy on him) was asked:
Is it permissible to eat meat slaughtered by one who uses amulets?
He replied: That is subject to further discussion. If it is known that the one who uses amulets associates others with Allah and believes that the amulets themselves, not Allah, bring benefits and cause harm; or he relies on them instead of putting his trust in Allah; or he believes in the dead and calls upon them, seeks help from them and makes vows to them; or he believes in trees, idols or jinn, and calls upon them or seeks help from them - meat slaughtered by such a person is not to be eaten.
But if he uses them in a regular manner, and regards them as a means of bringing benefits, but he does not believe that they themselves cause harm or bring benefits, and he does not do any practices of shirk, then meat slaughtered by him may be eaten, because use of amulets in this case is a kind of minor shirk.
End quote from http://www.alifta.net
See also the answer to question no. 104111
And Allah knows best.
Reproduced from Islam QA