Who counts among the People of the Book whom a Muslim may marry?
Christians and Jews are without any doubt People of the Book, including Christians who believe in the Trinity. Anyone who holds to a revealed book is regarded as such in this world. How things truly stand with their faith and deeds is for God alone to judge.
The verse above expressly mentions the women of those who were given the Book before the Muslims. This means people who hold to a book that God revealed to a prophet. Jews and Christians clearly belong to this group, since they hold to the Torah and the Gospel.
Some ask whether this also applies to Christians who believe in the Trinity. The answer is yes. The Holy Qur’an gave this permission at a time when the Christians of Arabia held exactly this belief. It still called them People of the Book.
Behind this lies a simple principle. In this world, people are taken by what they say about themselves. There are Muslims, too, who do things that contradict the teachings of Islam, and yet they are still called Muslims. In the same way, someone who holds to a revealed book remains one of the People of the Book for us, even if their belief or conduct does not fully match that book.
Whether their faith stands before God is a different question. The second verse above says that God Himself will judge between the religions on the Day of Resurrection. That decision does not belong to human beings. On earth what counts is what a person professes. In the Hereafter what counts is what was truly in the heart.
For marriage this means a clear and broad rule. The verse requires a proper marriage, a dowry and a chaste woman. It does not require a detailed examination of her beliefs.