Marriage to a Jewish or Christian woman is permissible according to the view of the majority of scholars. Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (7/99):
There is no difference of opinion among the scholars concerning the permissibility of marrying free women of the people of the Book. Among those from whom this view was narrated are ‘Umar, ‘Uthmaan, Talhah, Hudhayfah, Salmaan, Jaabir, and others.
Ibn al-Mundhir said: There is no sound narration from any of the earliest generation to suggest that this is haraam. Al-Khallaal narrated, with his isnaad, that Hudhayfah, Talhah, al-Jaarood ibn al-Mu’alla and Udhaynah al-‘Abdi all married women from among the people of the Book. This was also the view of the rest of the scholars.
The main evidence concerning that is the verse in which Allaah says (interpretation of the meaning):
“Made lawful to you this day are At Tayyibaat [all kinds of Halaal (lawful) foods, which Allaah has made lawful (meat of slaughtered eatable animals, milk products, fats, vegetables and fruits)]. The food (slaughtered cattle, eatable animals) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians) before your time when you have given their due Mahr (bridal-money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as girlfriends. And whosoever disbelieves in Faith, [i.e. in the Oneness of Allaah and in all the other Articles of Faith i.e. His (Allaah’s) Angels, His Holy Books, His Messengers, the Day of Resurrection and Al Qadar (Divine Preordainments)], then fruitless is his work; and in the Hereafter he will be among the losers”
What is meant by muhsanah (translated here as chaste) is free and chaste women. Ibn Katheer (may Allaah have mercy on him) said in his Tafseer:
This is the view of the majority here, and this is what appears to be the case; lest she not only be a dhimmiyah but also unchaste, in which case she will be totally corrupt and her husband will end up as described in the proverb, “He bought bad dates and was cheated in weights and measures too”. The apparent meaning of the verse is that what is meant by al-muhsanaat (chaste women) is women who refrain from zina, as Allaah says in another verse (interpretation of the meaning):
“they (the above said slave-girls) should be chaste [muhsanaat], not committing illegal sex, nor taking boyfriends”
The Christians and Jews are kuffaar and mushrikeen, according to the Qur’aan, but they are excluded from the prohibition on marrying their women, because Allaah says (interpretation of the meaning):
“And do not marry Al-Mushrikaat (idolatresses) till they believe (worship Allaah Alone). And indeed a slave woman who believes is better than a (free) Mushrikah (idolatress), even though she pleases you”
This is the clearest way of reconciling between the two verses.
Allaah has described them as being mushrikeen as He says (interpretation of the meaning):
“They (Jews and Christians) took their rabbis and their monks to be their lords besides Allaah (by obeying them in things which they made lawful or unlawful according to their own desires without being ordered by Allaah), and (they also took as their Lord) Messiah, son of Maryam (Mary), while they (Jews and Christians) were commanded [in the Tawraat (Torah) and the Injeel (Gospel)] to worship none but One Ilaah (God — Allaah) Laa ilaaha illa Huwa (none has the right to be worshipped but He). Praise and glory be to Him (far above is He) from having the partners they associate (with Him)”
So they are kuffaar and mushrikeen, but Allaah has permitted us to eat their meat and to marry their women if they are chaste. This is an exemption from the general meaning of the verse in Soorat al-Baqarah.
But it should be noted that it is better and safer not to marry women of the people of the Book, especially nowadays. Ibn Qudaamah (may Allaah have mercy on him) said: “… as this is the case, it is better not to marry a woman of the people of the Book, because ‘Umar said to those who married women of the people of the Book: ‘Divorce them,’ so they divorced them, except Hudhayfah. ‘Umar said to him: ‘Divorce her.’ (Hudhayfah) said: ‘Do you bear witness that she is haraam?’ He said: ‘She is a live coal, divorce her.’ He said: ‘Do you bear witness that she is haraam?’ He said: ‘She is a live coal.’ He said: ‘I know that she is a live coal, but she is permissible for me.’ A while later, he divorced her and it was said to him: ‘Why did you not divorce her when ‘Umar commanded you to?’ He said: ‘I did not want the people to think that I had done something wrong (by marrying her).’ Perhaps he was fond of her or perhaps they had a child together so he was fond of her.”
Shaykh Ibn Baaz (may Allaah have mercy on him) said: “If the woman of the people of the Book is known to be chaste and to keep away from the means that lead to immorality, it is permissible, because Allaah has permitted that and has permitted us to marry their woman and eat their meat.
“But nowadays there is the fear that those who marry them may be faced with much evil. They may call him to their religion and that may lead to their children being raised as Christians. So the danger is very real and very serious. To be on the safe side, the believer should not marry them. And in most cases there is no guarantee that the woman will not commit immoral actions, or bring along children from a previous relationship… but if the man needs to do that then there is no sin on him, so that he can keep himself chaste and lower his gaze by being married to her. He should strive to call her to Islam and beware of her evil and of allowing her to drag him or the children towards kufr.”
Fataawa Islamiyyah, 3/172
And Allaah knows best.