Is it obligatory to maintain ties of kinship with a polytheist, and not obligatory to maintain ties of kinship with a disbeliever?

The ruling concerning the treatment of a disbeliever and a polytheist is the same. The more preponderant view is that maintaining ties of kinship with them is not obligatory but permissible, except for parents, whose companionship with kindness is obligatory, based on the Almighty's saying: "But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness." And based on the Prophet's (peace and blessings be upon him) saying to Asma concerning her polytheist mother: "Maintain ties with your mother." This is the madhhab of the majority of jurists.