The Quran in chapter five, verse five says what means: This now at least refers to the Jews and Christians and it could refer to other communities as well who are based on a scriptural faith, as opposed to let’s say primal religions that do not necessarily follow what Muslims would deem to be a revealed scripture such, as the Old and New Testaments.
Naturally this question only arises in our modern context in which Muslims and non-Muslims are in interaction; people fall in love, and they want to get married; and now they are asking: Why can’t we?
For a Muslim man to marry a non-Muslim woman who is deemed to be a person from the People of the Book, Christian or Jew, many Muslim scholars say that this is permissible.
He should remain on good terms with her and keep exerting his utmost so as to persuade her to return to the right path of Islam.
If he is already sincere in his attempts to do so, Almighty Allah will help him and may guide the man his daughter married to the right path.
This problem should be tackled seriously from all sides.