Is it permissible for a girl who is subjected to severe injustice, beatings, humiliation, and accusations concerning her honor from her parents, to reduce her interaction and conversation with them, without mistreating them, if their closeness harms her health?

Your parents' ill-treatment of you and their accusation regarding your honor is a serious and strange matter, for their natural disposition should be compassion towards their children, especially daughters.

Seek the reason for this treatment and try to remedy it. Request intercession on your behalf from someone who holds a respected position with them.

You have done well by enduring patiently, by showing them piety, and by praying for them. Know that raising your voice at them is a reprehensible act, and you must repent from it.

There is no blame upon you for keeping your distance from them and minimizing conversation with them to the extent that it wards off their harm, while continuing to show them piety and benevolence, such as praying for them and checking on their well-being. Piety (birr) is delivering as much good as possible and warding off as much harm as possible.