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)”
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.