Is it permissible to go out with a sister who does not wear hijab (is unchaste in dress) in public places, knowing that not going out with her could lead to a near severance of ties with the family?

It is permissible to go out with a woman who is immodestly dressed, provided certain conditions are met. This outing can be utilized to offer advice and remind everyone of what increases faith and encourages performing acts of obedience and abandoning sins. Al-Bukhari narrated from Aisha, may Allah be pleased with her, that she said: "Indeed, the first thing that was revealed from it was a surah from Al-Mufassal, containing mention of Paradise and Hell. Then, when people returned to Islam, lawful and unlawful matters were revealed."

If the immodestly dressed woman does not repent, then ostracizing her is permissible if a benefit is hoped from it; otherwise, it is better to abandon it. Ostracization does not contradict the questioner going out with the family, especially since his refusal to go out has led to a near estrangement.