To answer the question as to whether the meat sold in the markets or served in restaurants is lawful for Muslims to consume, one needs to carefully look at two points: 1. Who has slaughtered the animal (the slaughterer)?
The slaughterer must be from the People of the Book (i.e. a Christian or a Jew). Animals slaughtered of other religions or people with no religion at all are not lawful for Muslims to consume. Hence, for the meat sold in a Non-Muslim market, one should find out whether the religion of the slaughterer is either Christianity or Judaism.