Praise be to Allaah.

It is permissible for a Muslim man to marry a woman from among the People of the Book, a Jewish or Christian woman, but not a woman from any other kaafir religion, as 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)…”

[al-Maa’idah 5:5]

This refers to chaste women from among the People of the Book, not immoral women. It is not permissible for a Muslim woman to marry a mushrik who is not a Muslim, no matter what his religion is. Allaah says (interpretation of the meaning): 

“And give not (your daughters) in marriage to Al-Mushrikoon till they believe (in Allaah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire…”

[al-Baqarah 2:221]

And because Islam should prevail and not be prevailed over, as is stated in the religion of Islam. 

Shaykh ‘Abd al-Kareem al-Khudayr

It is known that the man is the stronger party and the one who dominates the lives of the family, his wife and children. So it is not wise for a Muslim woman to marry a kaafir man who will dominate her life and the life of her children, the consequences of which will be very serious, as there is the possibility that he may divert her from her religion and raise the children in his own religion. 

And Allaah knows best.