The Quran

اليَومَ أُحِلَّ لَكُمُ الطَّيِّباتُ ۖ وَطَعامُ الَّذينَ أوتُوا الكِتابَ حِلٌّ لَكُم وَطَعامُكُم حِلٌّ لَهُم ۖ وَالمُحصَناتُ مِنَ المُؤمِناتِ وَالمُحصَناتُ مِنَ الَّذينَ أوتُوا الكِتابَ مِن قَبلِكُم إِذا آتَيتُموهُنَّ أُجورَهُنَّ مُحصِنينَ غَيرَ مُسافِحينَ وَلا مُتَّخِذي أَخدانٍ ۗ وَمَن يَكفُر بِالإيمانِ فَقَد حَبِطَ عَمَلُهُ وَهُوَ فِي الآخِرَةِ مِنَ الخاسِرينَ

Muhammad Asad

Today, all the good things of life have been made lawful to you. And the food of those who have been vouchsafed revelation aforetime is lawful to you,¹ and your food is lawful to them. And [lawful to you are], in wedlock, women from among those who believe [in this divine writ], and, in wedlock, women from among those who have been vouchsafed revelation before your time -provided that you give them their dowers, taking them in honest wedlock, not in fornication, nor as secret love-companions.² But as for him who rejects belief [in God] - in vain will be all his works: for in the life to come he shall be among the lost.³

This permission to partake of the food of the followers of other revealed religions excludes, of course, the forbidden categories of meat enumerated in verse 3 above. As a matter of fact, the Law of Moses, too, forbids them explicitly; and there is no statement whatsoever in the Gospels to the effect that these prohibitions were cancelled by Jesus: on the contrary, he is reported to have said, "Think not that I have come to destroy the Law [of Moses]... : I am not come to destroy, but to fulfil" (Matthew v, 17). Thus, the latitude enjoyed by post-Pauline followers of Jesus in respect of food does not correspond to what he himself practiced and enjoined.
Whereas Muslim men are allowed to marry women from among the followers of another revealed religion, Muslim women may not marry non-Muslims: the reason being that Islam enjoins reverence of all the prophets, while the followers of other religions reject some of them - e.g., the Prophet Muhammad or, as is the case with the Jews, both Muhammad and Jesus. Thus, while a non-Muslim woman who marries a Muslim can be sure that - despite all doctrinal differences - the prophets of her faith will be mentioned with utmost respect in her Muslim environment, a Muslim woman who would marry a non-Muslim would always be exposed to an abuse of him whom she regards as God's Apostle.
The above passage rounds off, as it were, the opening sentences of this surah, "O you who have attained to faith, be true to your covenants" - of which belief in God and the acceptance of His commandments are the foremost. It is immediately followed by a reference to prayer: for it is in prayer that man's dependence on God finds its most conscious and deliberate expression.