Surprising to me, all schools of thought prohibited a Muslim woman from marrying a man who is a kitabi (among the people of the book).I am not aware of a single dissenting opinion on this, which is rather unusual for Islamic jurisprudence because Muslim jurists often disagreed on many issues, but this is not one of them.
I was at a Muslim Sister's Fashion Show (predominately African American sisters) when during casual conversation a young sister (mid 20s) stated that her husband is Christian. She was under such a heavy attack that I could not get that question in.
However this issue is one that I need to understand because I can't adequately explain why there is a prohibition for the Muslim female in marrying from the people of the book and there is no prohibition for the Muslim male.
Importantly, the Hanafi, Maliki, and Shafi'i jurists held that it is reprehensible (makruh) for Muslim men to marry a kitabiyya if they live in non-Muslim countries.
They argued that in non-Muslim countries, mothers will be able to influence the children the most.
The argument goes: If men needed to be given express permission to marry a kitabiyya, women needed to be given express permission as well, but since they were not given any such permission then they must be barred from marrying a kitabi.