It is permissible to marry women from among the People of the Book. Allah says (what means):
And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you (Quran 5:5)
Ibn Qudamah (may Allah have mercy on him) said: There is no dispute between the people of knowledge, praise be to Allah, concerning the permissibility of marrying the free women from among the People of the Book. Of those from whom this is narrated are: 'Omar, Othman, Talhah, Huthaifah, Salman, Jabir and others. Ibn al Munthir said: It is not correct that any of the earlier (scholars) prohibited this. End quote, al-Mughni (7:500)
2. If a woman accepts Islam then apostates to the Jewish or Christian religion, she must be asked to repent; if she repents and returns to Islam, then all praise is for Allah, otherwise she is an apostate and all the rules which apply to apostates apply to her as agreed upon by the scholars (may Allah have mercy on them). See the answer to question 14231.
Therefore, it is necessary to advise this woman and remove any doubts, if she has doubts. This task should be undertaken by specialists from among the people of knowledge. If she insists on her apostasy, it is not lawful for a Muslim to marry her since marriage to an apostate is not valid by consensus.
If an individual affirms the oneness of Allah then it is easy to convince them of Islam, for the prophethood of our Prophet (may the peace and blessings of Allah be upon him) is established through tens of evidences. The doubts raised by the opponents of Islam around prophethood or the laws of the Sharee'ah have been responded to over the ages with responses which are convincing to any intelligent person. However, a person may be faced with a doubt and does not find anyone who can remove it for them and this could be the reason for their deviation. Therefore, we emphasize that people of knowledge should sit with this woman in the hope that Allah will guide her heart and inspire her to the truth and save her from the Fire.
Reproduced from Islam QA