Regarding this question, we’d like to cite the words of the eminent Muslim scholar Sheik Yusuf Al-Qaradawi:

Islam has made marriage to Jewish or Christian women lawful for Muslim men, for they are Ahl al-Kitab, that is, People of the Book, or people whose tradition is based upon a divinely revealed Scripture. Although they have distorted and altered it, they do possess a religion of divine origin, and hence Islam has made some exceptions in dealing with them. The Qur’an says: “…And the food of those who were given the Scripture (before you) is permitted to you and your food is permitted to them. And (lawful to you in marriage are) chaste women from the Believers and chaste women from those who were given the Scripture before you, when you give them their due cowers, desiring chastity, not lewdness or secret intrigues…” (Al-Ma’idah: 6)

Tolerance of such a degree is a characteristic of Islam which is hardly to be found among other faiths and nations. Despite the fact that Islam takes the People of the Book to task for their unbelief and error, it permits the Muslim to marry a Christian or Jewish woman who may, as his consort, the mistress of his house, the mother of his children, the source of his repose, and his companion for life, retain her own faith—all this, while the Qur’an says concerning marriage and its mystique: “And among His signs is that He created for you mates from among yourselves, that you may dwell with them in tranquility, and He has put love and mercy between you…” (Ar-Rum: 21)

However, a warning is in order here. In order of preference, a believing, practicing Muslim woman who loves her religion is preferable to a nominal Muslim woman who has inherited Islam from her parents. The Prophet (peace and blessings be upon him) said, “Get the one who is religious and prosper.” (Reported by al-Bukhari)

It is also obvious that a Muslim woman, regardless of who she is, is better suited to a Muslim man than a woman of Christian or Jewish faith, regardless of her merits. If a Muslim man has the slightest suspicion that a non-Muslim wife might affect the beliefs and attitudes of his children, it becomes obligatory on him to exercise caution.
If the number of Muslims in a country is small—for example, if they are immigrants residing in a non-Muslim country—their men ought to be prohibited from marrying non-Muslim women because, since Muslim women are prohibited from marrying non-Muslim men, their marriage to non-Muslim women means that many Muslim girls will remain unmarried. Since this situation is injurious to the Muslim society, this injury can be avoided by temporarily suspending this permission.

In this regard, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, adds:

Although religiously speaking, there is a permission granted for Muslims to marry women belonging to the People of the Book (i.e. the Christians and Jews), this permission cannot be generalized. Even during the time of the second Caliph, `Umar ibn al-Khattab, we read in the sources that he had forbidden some of the eminent Companions of the Prophet from marrying women of the People of the Book. He asked those Companions: “If everyone were to make use of this provision who would marry Muslim girls?”

For Caliph `Umar then it was only a question of Muslim women remaining unmarried. For us today, there are other complications arising out of such marriages.

Our experience with such marriages in North America compels us to conclude that after the initial phase of honey-moon, problems, often intractable, may arise when the couples settle down to start the business of living together and founding a family: Such nagging issues include: Which religious festivals to celebrate; what type of foods should we eat, how the children are to be brought up—issues that pose serious challenges in marriage. It is not uncommon to see that sometimes a father is even prevented from praying in front of his own children, while they are regularly taken to churches on a weekly basis. It is therefore not at all surprising when we see that vast majority of such marriages do end up in court.

The heavy toll of such marriages on children need not be over emphasized: The absence of a unified spiritual vision is bound to produce a generation of confused people who are totally deprived of any religious vision or ideals. Thus in the final analysis: Such marriages cost dearly spiritually, financially and emotionally.