May the peace, mercy and blessing of Allah be upon you,

All praise is due to Allah and may peace and blessing be upon the Messenger of Allah, his family, companions and whoever follows his guidance. To proceed:

Know (may Allah show mercy to us and to you) that for a Muslim man to marry a Christian or Jewish woman was not made permissible in the first place except in hopes that she would enter Islam, so if this benefit is not achieved, or worse, it is expected that there will be negative effects, not on the Muslim man alone, but also on his Muslim children and descendants to come, especially in this day and age, he would be advised to avoid this and he should be cautious about it. In fact, if disadvantages are expected to be predominant, then it would be prohibited for him to marry her; and why not when the Prophet (saws) has said about Muslim women, "A woman is married for four [reasons]: for her wealth, her lineage [good family], her beauty and her religious faith. So, marry the religious one and may you be blessed." [Agreed upon]

The Prophet (saws) also said, "There is no harm [in Shari`ah] and there should be no harm [from believers]." [Transmitted by Imam Ahmad and Ibn Majah, classed as good (hasan) by Shaikh al-Albani (may Allah Almighty have mercy on him), and with translation based on the explanation of Imam al-Nawawi]

A difference of religion, between Islam and disbelief, is one of the factors that prevent guardianship in marriage, according to the agreement of all four juristic schools. A disbelieving man cannot give his womenfolk in marriage if they are Muslim and a Muslim man cannot give his womenfolk in marriage if they are disbelievers. This is due to the Saying of Allah (in meaning),

{…they are but awliya' (friends, protectors, helpers) to one another.}

[Al-Ma'idah 5:51]

And also,

{Verily, your Wali (Protector or Helper) is Allah, His Messenger, and the believers…}

[Al-Ma'idah 5:55]

All of them made an exception for a Muslim man to marry off his disbelieving slave-woman (because he marries her off on the basis of ownership, not guardianship) and for the Muslim ruler (or his deputy) to marry off a disbelieving woman (if there is some difficulty with her own personal guardian). That is because his guardianship is general over all inhabitants of the Islamic realm and since she [the disbelieving woman] is one of the inhabitants, he bears the responsibility of guardianship over her, just as he does for the Muslim woman.

If a Muslim man marries a dhimmi (Jewish or Christian) woman, her disbelieving guardian should marry her to him; this is the madhhab (school) of the majority. It would not be wrong for the imam of the community or the Islamic center to assume guardianship and give her in marriage if her guardians refuse to do so, since he takes the place of the Islamic ruler in the lands of Islam, as long as he considers the pros and cons of the situation so as not to bring harm upon the Muslim community.

And Allah Almighty is more Exalted and He knows best.