Is it obligatory to continue advising one's parents when they wrong others, or is silence, coupled with not committing injustice oneself, sufficient, and is it enough to supplicate for them and not act as they do?

Praying for one's parents is always desirable and required. They should be advised gently and kindly when one observes them committing a transgression. It is not permissible to sit with them while they are engaging in backbiting or forbidden acts, except to condemn those acts. The right of parents to kindness and good treatment never lapses, no matter what they do. Allah has commanded kindness to parents even if they strive to persuade their child to polytheism, as affirmed by His 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." One must be careful not to harbor ill thoughts about them or to seek out their faults.