I have a question about the ruling concerning the eating of meat which is not halal. For years I have heard conflicting things. Some claim that we could only eat Christian meat back in the times when they used to kill their meat religiously and others say that it is okay to eat it no matter what.

The basic principle is that it is prohibited to eat the meat of animals other than those made lawful by the Shari'ah [En. Islamic law] and which are slaughtered by either Muslims or the People of the Book. Therefore, the permissibility of eating the meat of animals slaughtered by the People of the Book cannot be removed by doubt.

Ruling

The principle is that it is permissible to eat from the meat of the people of the Book unless one is certain that the animal was slaughtered by a non-Christian or a non-Jew or that it was beaten to death or electrocuted. But if one is not certain, the permissibility prevails.
- Evidence:
A Jewess offered the Prophet [peace and blessing be upon him] [the meat of a cooked sheep]. He ate from it without asking the manner of its slaughter or whether God's name was mentioned over it.
Based on the above:

The principle in Shari'ah is to think well of people. Hence, when one is in a country where the majority of its people are from the People of the Book it is unlawful to be overly particular and delve into matters.
God says in Surat al-Ma'idah:

Oh you who believe! Do not ask about matters which, if made known to you, might make things difficult for you… [5:101].

In his commentary on this verse, Ibn Katheer said: "God Almighty instructs His believing servants and prohibits them from asking about matters which do not benefit them … the apparent meaning of this verse is to prohibit asking about matters which, if made clear, may create hardship for the inquirer so it is better to refrain from asking about them." Hence, it is disliked to delve into the heart of a matter. Haritha ibn al-Nu'man (may God be pleased with him) reported that the Prophet (peace and blessings be upon him) said: "Whenever ill thoughts creep into your mind, do not engage yourself in verifying them."