Is it permissible to sever ties with relatives, not visit them, and avoid speaking with them to avoid the sins they commit, such as being lenient in private intermingling [between sexes], backbiting, or speaking in a way that incites lusts, or because some of them do not pray or disbelieve in God?

It is not permissible to sit with relatives or others while they are committing a sin, such as backbiting, forbidden speech, or disbelief, as the one who sits with them becomes a partner in sin if he does not object to them. However, this does not justify cutting off ties of kinship. Rather, one must maintain kinship ties with kindness, which is not limited to visits but also includes calls, correspondence, and greetings. The greatest forms of maintaining ties are enjoining good, forbidding evil, and offering advice. If you are unable to change the wrongdoing, then stop sitting with them, and continue to maintain ties with them in whatever way you can to absolve yourself of responsibility.