What is the effect of a Christian mother not embracing Islam on the children, and does Islam approve of a Muslim man marrying a Christian woman?

Allah has permitted a Muslim man to marry a chaste woman from among the People of the Book, based on His saying, the Most High: "and chaste women from among the believers and chaste women from among those who were given the Scripture before you." However, if she is not chaste, then marriage to her is not permissible. It is preferable for a Muslim man to marry a Muslim woman because she will raise the children according to Islam, and the risk of them being influenced by the faith of the Woman of the Book will be removed. Furthermore, there is a prevalence of women from the People of the Book abandoning their religion and embracing atheism or lacking chastity. Children follow the religion of their Muslim father, based on His saying, the Most High: "And whoever desires a religion other than Islam, it will never be accepted from him, and in the Hereafter he will be among the losers." It does not harm a righteous Muslim that his mother is not Muslim, based on His saying, the Most High: "And no bearer of burdens will bear the burden of another." It is obligatory to treat a non-Muslim mother with kindness, as long as she does not call to disobedience, based on His saying, the Most High: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness." And she should be invited to Islam.