After Allah mentioned the filthy things that He prohibited for His believing servants and the good things that He allowed for them, He said next,

﴿الْيَوْمَ أُحِلَّ لَكُمُ الطَّيِّبَـتُ﴾

(Made lawful to you this day are At-Tayyibat.) Allah then mentioned the ruling concerning the slaughtered animals of the People of the Book, the Jews and Christians,

﴿وَطَعَامُ الَّذِينَ أُوتُواْ الْكِتَـبَ حِلٌّ لَّكُمْ﴾

(The food of the People of the Scripture is lawful to you..) meaning, their slaughtered animals, as Ibn `Abbas, Abu Umamah, Mujahid, Sa`id bin Jubayr, `Ikrimah, `Ata', Al-Hasan, Makhul, Ibrahim An-Nakha`i, As-Suddi and Muqatil bin Hayyan stated. This ruling, that the slaughtered animals of the People of the Book are permissible for Muslims, is agreed on by the scholars, because the People of the Book believe that slaughtering for other than Allah is prohibited. They mention Allah's Name upon slaughtering their animals, even though they have deviant beliefs about Allah that do not befit His majesty. It is recorded in the Sahih that `Abdullah bin Mughaffal said, "While we were attacking the fort of Khaybar, a person threw a leather bag containing fat, and I ran to take it and said, `I will not give anyone anything from this container today.' But when I turned I saw the Prophet (standing behind) while smiling.'' The scholars rely on this Hadith as evidence that we are allowed to eat what we need of foods from the booty before it is divided. The scholars of the Hanafi, the Shafi`i and the Hanbali Madhhabs rely on this Hadith to allow eating parts of the slaughtered animals of the Jews that they prohibit for themselves, such as the fat. They used this Hadith as evidence against the scholars of the Maliki Madhhab who disagreed with this ruling. A better proof is the Hadith recorded in the Sahih that the people of Khaybar gave the Prophet a gift of a roasted leg of sheep, which they poisoned. The Prophet used to like eating the leg of the sheep and he took a bite from it, but it told the Prophet that it was poisoned, so he discarded that bite. The bite that the Prophet took effected the palate of his mouth, while Bishr bin Al-Bara' bin Ma`rur died from eating from that sheep. The Prophet had the Jewish woman, Zaynab, who poisoned the sheep, killed. Therefore, the Prophet and his Companions wanted to eat from that sheep and did not ask the Jews if they removed what the Jews believed was prohibited for them, such as its fat. Allah's statement,

﴿وَطَعَامُكُمْ حِلٌّ لَّهُمْ﴾

(and your food is lawful to them.) means, you are allowed to feed them from your slaughtered animals. Therefore, this part of the Ayah is not to inform the People of the Scriptures that they are allowed to eat our food -- unless we consider it information for us about the ruling that they have -- i. e, that they are allowed all types of foods over which Allah's Name was mentioned, whether slaughtered according to their religion or otherwise. The first explanation is more plausible. So it means: you are allowed to feed them from your slaughtered animals just as you are allowed to eat from theirs, as equal compensation and fair treatment. The Prophet gave his robe to `Abdullah bin Ubayy bin Salul, who was wrapped with it when he died. They say that he did that because `Abdullah had given his robe to Al-`Abbas when Al-`Abbas came to Al-Madinah. As for the Hadith,

«لَا تَصْحَبْ إِلَّا مُؤْمِنًا، وَلَا يَأْكُلْ طَعَامَكَ إِلَّا تَقِي»

(Do not befriend but a believer, nor should other than a Taqi (pious person) eat your food.), This is to encourage such behavior, and Allah knows best.