What is the basis in Shari'ah for the widely accepted prohibition on Muslim women marrying 'chaste men of the people of the book?'

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

1 - All the jurists agreed in a consensus that a Muslim woman cannot marry a Non-Muslim man. Allah Says (what means): {And do not marry polytheistic men [to your women] until they believe.} [Quran 2:221]

Allah also Says (what means): {O you who have believed, when the believing women come to you as emigrants, examine them. Allah is most knowing as to their faith. And if you know them to be believers, then do not return them to the disbelievers; they are not lawful [wives] for them, nor are they lawful [husbands] for them.} [Quran 60:10]

Because in this marriage, a Muslim woman faces the danger of Kufr (disbelief), as her husband might influence her. A wife always follows the footprints of her husband.

2 – On these bases, the marriage of a Muslim woman is prohibited with any Non-Muslim man either he is a Christian, a Jew, an Atheist or an Idolater, etc... Allah has invalidated the guardianship of a non-Muslim over any Muslim. Allah Says (what means): {…and never will Allah give the disbelievers over the believers a way [to overcome them].} [Quran 4:141]

3- All the jurists agree that marriage of a Muslim man to a Chaste woman from the People of the Book is lawful. Some of them disliked it. The People of the Book means the people of the Torah and the Bible, who believe in a revealed religion whose origin was true, like Judaism and Christianity. Allah Says (what means): {This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them. And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you, when you have given them their due compensation, desiring chastity, not unlawful sexual intercourse or taking [secret] lovers.} [Quran 5:5] The main condition for marriage is the chastity of the woman, because this will be a cause of love and affection between spouses.

4 – A Muslim can not marry a polytheistic woman (who worships anything other than Allah, like Idols, Stars, Sun) or an atheistic woman or an apostate woman. Allah Says (what means): {And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember.} [Quran 2:221]

5 – The reason for the permissibility of marriage to a woman of the People of the Book is that she also believes in the basics of Islam, like her faith in the Oneness of Allah, in the Hereafter, and in the reward and punishment from Almighty Allah. There are some linking bridges between them, which may assure a happy conjugal life, and it is expected that she would embrace Islam, because she believes in the Messengers and in the revealed books in general.

For more benefit, please refer to Fataawa 384922, 397159, and 84159.

Allah knows best.