Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Islam has given the woman the right to study and be educated in a similar way to men.
Anas (Radiya Allahu Anhu) said that the Prophet (Sallallahu Alaihi wa Sallam) said, “Seeking knowledge is obligatory upon each and every Muslim”. [Reported by Ibn Majah, and Albani said that ‘it is an authentic Hadith’]
The saying of the Prophet (Sallallahu Alaihi wa Sallam) “Upon each and every Muslim” includes males and females.
As seeking knowledge is permitted by the Shariah, then there is no harm for a woman to go out to seek knowledge as long as she adheres to the Islamic requirements; like Hijab, no mixing (of males and females), not speaking in a soft or attractive manner, and with the permission of her husband.
There is no difficulty for a woman to learn the religious aspects of her religion. The matter is easy and the ways of seeking knowledge are many. There are many recorded materials on religion that a woman can listen to at home, and she can go out to seek knowledge but with the religious requirements already mentioned, by attending lectures organized by women, or general lectures, and so on.
Allah knows best.