Praise be to Allah.
The Muslims are unanimously agreed that it is not permissible for a Muslim woman to marry a non-Muslim, whether he is Jewish, Christian or anything else, because Allah, may He be exalted, says (interpretation of the meaning):
“And give not (your daughters) in marriage to Al-Mushrikoon till they believe (in Allah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater, etc.), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire, but Allah invites (you) to Paradise and Forgiveness by His Leave, and makes His Ayat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember”
“…then if you ascertain that they are true believers, send them not back to the disbelievers, they are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them”
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: The Muslims are agreed that a non-Muslim cannot inherit from a Muslim, and a non-Muslim man cannot marry a Muslim woman.
End quote from al-Fataawa al-Kubra (3/130).
Moreover, “Islam is to prevail and is not to be prevailed over,” as the Prophet (blessings and peace of Allah be upon him) said.
Narrated by ad-Daaraqutni; classed as hasan by al-Albaani in Saheeh al-Jaami‘ (no. 2778)
The man is in a position of leadership over the woman, and it is not permissible for a non-Muslim to be in a position of leadership over a Muslim woman, because Islam is the true religion and all other religions are false.
If a Muslim woman marries a non-Muslim man, knowing the ruling thereon, then she is a zaaniyah and is subject to the hadd punishment for zina. If she was unaware of the ruling, then she is excused, but they must be separated, with no need for talaaq (divorce), because the marriage is invalid in the first place.
Based on that, the Muslim woman whom Allah has honoured with Islam and her guardian must beware of that and adhere to the limits set by Allah, and be proud of being Muslims. Allah, may He be exalted, says (interpretation of the meaning):
“Whosoever desires honour, power and glory then to Allah belong all honour, power and glory (and one can get honour, power and glory only by obeying and worshipping Allah (Alone))”
We advise this woman to end her relationship with that Christian man, because it is not permissible for a woman to form a relationship with a man who is a non-mahram to her. This has been discussed previously in the answer to question no. 23349
But if he chooses to become Muslim willingly and voluntarily, then there is nothing wrong with her marrying him, if her guardian agrees to that.
However, we advise what the Prophet (blessings and peace of Allah be upon him) instructed, which is that she should choose for herself someone who is religiously committed and of good character.
We ask Allah, may He be exalted, to set her affairs straight and guide her.
For more information, please see the answer to question no. 83736.