Is it obligatory for a Muslim to seek his mother's permission before leaving the house to perform a Sharia-compliant act, such as enjoining good, and what is the ruling if she has a slight fear for him?

If enjoining good is a communal obligation (fard kifayah), then permission from the mother is required if she forbids it, unlike an individual obligation (fard ayn). If the mother does not forbid it, then there is no harm. However, if she knows and becomes angry, then it is not permissible to do so unless the denunciation is individually incumbent (ta'ayyan al-inkar). The general principle is the obligation to satisfy the mother and the prohibition of angering her, unless she commands disobedience. If the mother does not know, then there is no harm, because you have not angered her and you have performed an act of obedience.