Has Islam called for women to be content with religious sciences to the exclusion of worldly sciences, and would you allow your daughters to pursue worldly sciences alongside religious ones?

A woman's pursuit of secular knowledge is, in principle, permissible. However, its ruling can shift to disliking (makrooh), prohibition (haram), recommendation (mustahabb), or obligation (wajib) depending on the nature of the study and the needs of society. If the study adheres to Islamic guidelines and society is in need of it, such as women becoming doctors, then her pursuing it is an act of worship pleasing to Allah. But if it does not adhere to guidelines, or if society does not need it, then her going out to study oscillates between disliking and prohibition. Nevertheless, religious sciences remain superior to secular sciences.