Making friends with a kaafir woman
Question

                Is it allowed for a muslim woman to be friends with a non-muslim woman who is very decent, without neglecting her one religion and is there a severe punishment if she does?
Praise be to Allah.
    Undoubtedly making friends with a kaafir woman will adversely 
    affect her religious commitment, because a kaafir woman does not behave in 
    the same manner or have the same attitude as a Muslim woman, and she does 
    not worship Allaah according to the religion of Islam. Therefore she will 
    not avoid doing things that may adversely affect this Muslim woman who may 
    be deceived by the modest dress or good manners of this kaafir woman, 
    especially in matters that will adversely affect her religious commitment. 

    Similarly, making friends with her may lead to some kind of 
    approval in one's heart for the rituals that she does as part of her own 
    religion, and this will weaken the sense of friendship and enmity for the 
    sake of Allaah (al-wala’ wa’l-bara’). 

    Indeed, it may lead some ignorant people to disapprove of the 
    ruling of Allaah that the kaafirs are disbelievers who will abide in Hell 
    forever – we seek refuge with Allaah. Hence the Prophet  (peace and 
    blessings of Allaah be upon him) said: “Do not keep company with anyone but 
    a believer and do not let anyone eat your food but one who is pious.” 
    (Narrated by al-Tirmidhi, 2395; Abu Dawood, 4832; classed as saheeh by Ibn 
    Hibbaan, 2/314; classed as hasan by Shaykh al-Albaani in Saheeh al-Jaami’, 
    7341). 
We do not mean, however, 
    that this Muslim woman should cut herself off completely from the kaafir 
    woman; she may visit with her, visit her when she is sick and give her 
    gifts, but without forming an emotional attachment or joining in their 
    festivals and celebrations. And the Muslim woman should aim, in those visits 
    and gift-giving, to call this kaafir woman to Islam. This is what our 
    Prophet  (peace and blessings of Allaah be upon him) did, as is 
    mentioned in two hadeeths: 

    1 – It was narrated from Sa’eed ibn al-Musayyib that his 
    father said: “When Abu Taalib was on his deathbed, the Prophet  (peace 
    and blessings of Allaah be upon him) entered upon him, and Abu Jahl and 
    ‘Abd-Allaah ibn Abi Umayyah were present. The Prophet  (peace and 
    blessings of Allaah be upon him) said, ‘O uncle, say Laa ilaaha 
    ill-Allaah, and I will plead for you before Allaah.’ Abu Jahl and 
    ‘Abd-Allaah ibn Abi Umayyah said: ‘O Abu Taalib, will you turn away from the 
    religion of ‘Abd al-Muttalib?’ The Prophet  (peace and blessings of 
    Allaah be upon him) said: ‘I will keep on praying for forgiveness for you 
    until I am forbidden (by Allaah) to do so.” Then the following aayah was 
    revealed: 
“It is not (proper) for 
    the Prophet and those who believe to ask Allaah’s forgiveness for the 
    Mushrikoon, even though they be of kin, after it has become clear to them 
    that they are the dwellers of the Fire (because they died in a state of 
    disbelief)”

    [al-Tawbah 9:113]

    Narrated by al-Bukhaari, 4398; Muslim, 24 

    2 – It was narrated that Anas (may Allaah be pleased with 
    him) said: “There was a Jewish boy who used to serve the Prophet  (peace 
    and blessings of Allaah be upon him), and he fell sick. The Prophet  
    (peace and blessings of Allaah be upon him) came to visit him; he sat by his 
    head and said, ‘Become Muslim.’ The boy looked at his father, who was 
    present, and he (the father) said: ‘Obey Abu’l-Qaasim  (peace and 
    blessings of Allaah be upon him).’ So he became Muslim, and the Prophet  
    (peace and blessings of Allaah be upon him) left, saying, ‘Praise be to 
    Allaah Who has saved him from the Fire.’” 

    Narrated by al-Bukhaari, 1290. 

    The Prophet  (peace and blessings of Allaah be upon him) 
    gave permission to Asma’ bint Abi Bakr to receive her mushrik mother (when 
    she came to visit her), and ‘Umar (may Allaah be pleased with him) gave a 
    gift of a garment to his mushrik brother. 

    It was narrated that Asma’ bint Abi Bakr (may Allaah be 
    pleased with her) said: “My mother came to visit me at the time of the 
    Messenger of Allaah  (peace and blessings of Allaah be upon him), and 
    she was a mushrik. So I consulted the Messenger of Allaah,  (peace and 
    blessings of Allaah be upon him) and asked him, ‘My mother wants to visit me 
    and expects me to treat her kindly; should I uphold the ties of kinship with 
    my mother?’ He said, ‘Yes, uphold the ties of kinship with your mother.’” 

    Narrated by al-Bukhaari, 2477; Muslim, 1003 

    It was narrated that ‘Abd-Allaah ibn ‘Umar (may Allaah be 
    pleased with them both) said: “ ‘Umar ibn al-Khattaab saw a silken garment 
    being sold at the door of the mosque. He said, ‘O Messenger of Allaah, why 
    don’t you buy it and wear it on Fridays and when the delegations come to 
    you?’ He said, ‘This is worn by one who has no share in the Hereafter.’ 
    Later on some silken garments were brought and the Messenger of Allaah  
    (peace and blessings of Allaah be upon him) gave one to ‘Umar. He said, ‘Are 
    you giving me this to wear when you said what you said about the garment of 
    ‘Utaarid?’ He said, ‘I did not give it to you to wear.’ So ‘Umar gave it to 
    a mushrik brother of his in Makkah to wear.” 

    Narrated by al-Bukhaari, 2470; Muslim 2068. 

    Shaykh Saalih al-Fawzaan said: There is nothing wrong with 
    visiting kaafirs in order to call them to Islam. The Prophet  (peace and 
    blessings of Allaah be upon him) visited his paternal uncle Abu Taalib when 
    he was dying and called him to Islam, and he visited the Jewish boy and 
    called him to Islam. 

    But visiting kaafirs in order to have a good time with them 
    is not permitted, because it is obligatory to hate them and shun them. It is 
    permissible to accept their gifts because the Prophet  (peace and 
    blessings of Allaah be upon him) accepted gifts from some of the kaafirs, 
    such as the gift from al-Muqawqis the ruler of Egypt. But it is not 
    permissible to congratulate them on the occasion of their festivals because 
    this implies befriending them and approving of their falsehood.

     Al-Muntaqa min Fataawa al-Shaykh al-Fawzaan, 1/255

     And Allaah knows best.