Are the Jews and Christians who exist nowadays mushrikeen (polytheists) and is it permissible to marry their women?
Question

                What is the ruling on marrying a Jewish or Christian woman? Are the Jews and Christians of this age regarded as people of the Book or as mushrikeen?.
Praise be to Allah.Marriage to a Jewish or Christian woman is 
    permissible according to the view of the majority of scholars. Ibn Qudaamah 
    (may Allaah have mercy on him) said in al-Mughni (7/99): 
There is no difference of opinion among the 
    scholars concerning the permissibility of marrying free women of the people 
    of the Book. Among those from whom this view was narrated are ‘Umar, 
    ‘Uthmaan, Talhah, Hudhayfah, Salmaan, Jaabir, and others. 
Ibn al-Mundhir said: There is no sound 
    narration from any of the earliest generation to suggest that this is 
    haraam. Al-Khallaal narrated, with his isnaad, that Hudhayfah, Talhah, 
    al-Jaarood ibn al-Mu’alla and Udhaynah al-‘Abdi all married women from among 
    the people of the Book. This was also the view of the rest of the scholars.
    
The main evidence concerning that is the 
    verse in which Allaah says (interpretation of the meaning): 
“Made lawful to you this day are At Tayyibaat 
    [all kinds of Halaal (lawful) foods, which Allaah has made lawful (meat of 
    slaughtered eatable animals, milk products, fats, vegetables and fruits)]. 
    The food (slaughtered cattle, eatable animals) of the people of the 
    Scripture (Jews and Christians) is lawful to you and yours is lawful to 
    them. (Lawful to you in marriage) are chaste women from the believers and 
    chaste women from those who were given the Scripture (Jews and Christians) 
    before your time when you have given their due Mahr (bridal-money given by 
    the husband to his wife at the time of marriage), desiring chastity (i.e. 
    taking them in legal wedlock) not committing illegal sexual intercourse, nor 
    taking them as girlfriends. And whosoever disbelieves in Faith, [i.e. in the 
    Oneness of Allaah and in all the other Articles of Faith i.e. His (Allaah’s) 
    Angels, His Holy Books, His Messengers, the Day of Resurrection and Al Qadar 
    (Divine Preordainments)], then fruitless is his work; and in the Hereafter 
    he will be among the losers” 
[al-Maa'idah 5:5] 
What is meant by muhsanah (translated here as 
    chaste) is free and chaste women. Ibn Katheer (may Allaah have mercy on him) 
    said in his Tafseer: 
This is the view of the majority here, and 
    this is what appears to be the case; lest she not only be a dhimmiyah but 
    also unchaste, in which case she will be totally corrupt and her husband 
    will end up as described in the proverb, “He bought bad dates and was 
    cheated in weights and measures too”. The apparent meaning of the verse is 
    that what is meant by al-muhsanaat (chaste women) is women who refrain from 
    zina, as Allaah says in another verse (interpretation of the meaning):
    
“they (the above said slave-girls) should be 
    chaste [muhsanaat], not committing illegal sex, nor taking boyfriends”
    
[al-Nisa’ 4:25] 
The Christians and Jews are kuffaar and 
    mushrikeen, according to the Qur’aan, but they are excluded from the 
    prohibition on marrying their women, because Allaah says (interpretation of 
    the meaning): 
“And do not marry Al-Mushrikaat 
    (idolatresses) till they believe (worship Allaah Alone). And indeed a slave 
    woman who believes is better than a (free) Mushrikah (idolatress), even 
    though she pleases you” 
[al-Baqarah 2:221] 
This is the clearest way of reconciling 
    between the two verses. 
Allaah has described them as being mushrikeen 
    as He says (interpretation of the meaning): 
“They (Jews and Christians) took their rabbis 
    and their monks to be their lords besides Allaah (by obeying them in things 
    which they made lawful or unlawful according to their own desires without 
    being ordered by Allaah), and (they also took as their Lord) Messiah, son of 
    Maryam (Mary), while they (Jews and Christians) were commanded [in the 
    Tawraat (Torah) and the Injeel (Gospel)] to worship none but One Ilaah (God 
    — Allaah) Laa ilaaha illa Huwa (none has the right to be worshipped but He). 
    Praise and glory be to Him (far above is He) from having the partners they 
    associate (with Him)” 
[al-Tawbah 9:31] 
So they are kuffaar and mushrikeen, but 
    Allaah has permitted us to eat their meat and to marry their women if they 
    are chaste. This is an exemption from the general meaning of the verse in 
    Soorat al-Baqarah. 
But it should be noted that it is better and 
    safer not to marry women of the people of the Book, especially nowadays. Ibn 
    Qudaamah (may Allaah have mercy on him) said: “… as this is the case, it is 
    better not to marry a woman of the people of the Book, because ‘Umar said to 
    those who married women of the people of the Book: ‘Divorce them,’ so they 
    divorced them, except Hudhayfah. ‘Umar said to him: ‘Divorce her.’ 
    (Hudhayfah) said: ‘Do you bear witness that she is haraam?’ He said: ‘She is 
    a live coal, divorce her.’ He said: ‘Do you bear witness that she is 
    haraam?’ He said: ‘She is a live coal.’ He said: ‘I know that she is a live 
    coal, but she is permissible for me.’ A while later, he divorced her and it 
    was said to him: ‘Why did you not divorce her when ‘Umar commanded you to?’ 
    He said: ‘I did not want the people to think that I had done something wrong 
    (by marrying her).’ Perhaps he was fond of her or perhaps they had a child 
    together so he was fond of her.” 
Al-Mughni, 7/99 
Shaykh Ibn Baaz (may Allaah have mercy on 
    him) said: “If the woman of the people of the Book is known to be chaste and 
    to keep away from the means that lead to immorality, it is permissible, 
    because Allaah has permitted that and has permitted us to marry their woman 
    and eat their meat. 
“But nowadays there is the fear that those 
    who marry them may be faced with much evil. They may call him to their 
    religion and that may lead to their children being raised as Christians. So 
    the danger is very real and very serious. To be on the safe side, the 
    believer should not marry them. And in most cases there is no guarantee that 
    the woman will not commit immoral actions, or bring along children from a 
    previous relationship… but if the man needs to do that then there is no sin 
    on him, so that he can keep himself chaste and lower his gaze by being 
    married to her. He should strive to call her to Islam and beware of her evil 
    and of allowing her to drag him or the children towards kufr.” 
Fataawa Islamiyyah, 3/172 
And Allaah knows best.