Does Islamic law prohibit maintaining family relationships with a non-Muslim relative?

Islamic law does not prohibit maintaining family relationships with non-Muslim relatives. Quite the contrary, it encourages such relations, for the Prophet (peace and blessings be upon him) instructed Muslims to uphold family ties even with non-Muslims.

Allah Almighty says, “Had your Lord willed, He could have made all people one community; but they will continue to differ — except those upon whom your Lord has bestowed mercy, and for that He created them” (Quran, 11: 118–119). The Prophet (peace and blessings be upon him) commanded maintaining relations with non-Muslim relatives. Asma’, the daughter of Abu Bakr (may Allah be pleased with them both), narrated, “My mother came to visit me during the peace treaty with Quraysh, and she was a polytheist. I sought the opinion of the Messenger of Allah (peace and blessings be upon him) and said, ‘O Messenger of Allah, my mother came to visit me, desiring to see me. Should I maintain ties with her?’ He said, ‘Yes, maintain ties with your mother’” (Bukhari and Muslim).

Based on the above, Islamic law does not prohibit maintaining relations with non-Muslim relatives, and, in fact, encourages it, as the Prophet (peace and blessings be upon him) instructed upholding family bonds even with non-Muslims.

And Allah the Almighty knows best.