Is it an individual obligation (fardh 'ayn) to seek religious knowledge, such that obedience to one's father is not required if he forbids it?

Knowledge is divided into two categories: that which is obligatory upon every accountable individual, for which parental consent is not required, and that which is a communal obligation (fard kifayah). For the latter, obedience to parents is not binding if they command its abandonment, unless the individual intends to travel to seek it, in which case their permission is required. Or, if the parent has a legitimate reason for preventing it, such as fear of harm, then obedience to the parent becomes obligatory at that point.

Accordingly, the questioner's sister is permitted to go out to seek knowledge even if her parents do not approve, unless her father has a legitimate reason, such as his fear for her safety, in which case she must obey him. One must exercise extreme caution when disobeying a parent, and should not do so unless the permissible reason for such disobedience is clearly established.