All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There are two types of friendship with a non-Muslim. The first is friendship that requires affection or approval of their disbelief, and this is forbidden friendship, as Allah, the Almighty, says (what means): {You will not find a people who believe in Allah and the Last Day having affection for those who oppose Allah and His Messenger, even if they were their fathers or their sons or their brothers or their kindred...} [Quran 58:22]
The second type is friendship which may be due to some worldly interests, and for this reason, a Muslim may need to interact with non-Muslims without having affection for them and while disapproving of their religious beliefs, and declaring one's disassociation from them. This is permissible. Allah, the Exalted, says (what means): {Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.} [Quran 60:8]. In Saheeh al-Bukhari and Sahih Muslim, it is narrated from Asmaa' bint Abi Bakr that she said, “My mother came to me while she was still a polytheist during the time of the Prophet . I asked the Messenger of Allah ‘My mother has come to me and she is inclined towards Islam or she is eager to receive a reward, shall I maintain ties with her?’ He said, ‘Yes, maintain ties with your mother.’”
There is also a distinction between religious affection, which entails approval of falsehood and is prohibited, and worldly affection for a specific reason, such as the love for parents, and the like. This type of affection is permissible.
We advise you to strive to be a means of guiding your family by praying for their guidance, explaining the virtues of Islam to them, and treating them kindly.
Allah knows best.