Marrying non-Muslim women is a detailed issue; it is not permissible to marry pagans, communists or Buddhists.
It is permissible to marry the chaste women from the People of the Book; those amongst them who are known to be chaste and far from the mediums of fornication.
Nevertheless, avoiding this is better and safer. Because marrying one may lead a person to convert to Christianity, and may lead his children to being Christian. This is why ‘Umar ibnul Khataab and others disliked this, fearing the evil that may be drawn to a person because of it. But the basis is that it is permissible, as Allah - the Mighty and Majestic - said in His noble Book in Surat al Ma-idah:
Made lawful to you this day are At-Tayyibaat. 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 before you, when you have given them their dowry, desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as girlfriends.
So He permitted marrying the Muhsanaat from the People of the Book, and a Muhsanah is a free woman who is known to be chaste.
But how can this be known today? How can it be known that a woman is chaste in America or Britain or anywhere else? This is indeed dangerous.
My advice is that a Muslim shouldn’t marry them. But if you do find one who is chaste, and it is known that she is chaste, then this is permissible. But it is better not to because a person may convert to Christianity due to his love for her, or his children may become Christians, whether it is while he is alive or after his death wa laa Hawla wa laa Quwata illa billaah.
And may the Salaat and Salaam be upon the final Messenger and his companions.
الزواج بغير المسلمات فيه تفصيل . الوثنيات والشيوعيات لا يجوز ، وهكذا البوذيات لا يجوز .
أما بالكتابيات المحصنات المعروفات بالإحصان والعفة والبعد عن وسائل الزنا ، وهن محصنات ، فيجوز للمسلم نكاح المحصنة ، لكن ترك ذلك أفضل وأولى وأبعد عن الشر ؛ لأن زواجها قد يفضي به إلى التنصر ، وقد يفضي بأولادها إلى التنصر ، ولهذا كره ذلك عمر وجماعة خوفًا على الإنسان من شر ذلك ، وإلا فالأصل أنه حلال ، كما قال - جل وعلا - في كتابه الكريم في سورة المائدة