Sage Sankara says even women can realize truth if they persist.+

Many centuries back orthodoxy barred and restricted women from studying scriptures restricted women only to household and bearing children.  In modern days women are capable has more capable of grasping the truth like in the Vedic era.

Women Saints and Sages

Women saints and sages of India have been given less importance, for several reasons obvious to anyone studying history...

In the medieval period, women were confined to homes and according to some moral codes, women were not allowed to study scriptures and chant mantras while mantras were invoked as female deities or Goddesses.

The Vedic rishis had wives who were learned women and took part in philosophical discussions. The crippling social practices for women, considering them as inferior, unfit for scriptural studies were introduced by male-dominated societies...While women monastics or nuns were introduced in Buddhism; it was not a common practice to have nuns in Hindu monastic orders until recent times.

Sage Sankara has philosophical disputes and debates with an equally great scholar, Mandana Mishra.  Mishra's learned wife Bharathi served as the umpire. She was taken as the incarnation of Goddess of learning Saraswati.

If one realizes the words and the world in which we exist created out of single stuff, and that single stuff is consciousness then no word is required to explain the Soul, which is the ultimate truth, Brahman, or God.  All the words and experiences are of the duality. The duality is not reality.

Sage Sankara says and also in Vivekachoodamani, that even women can realize the truth if they persist. (Mand.P.351)

Thus, it proves that Sage Sankara wanted even women to acquire Advaitic wisdom, whereas the orthodox Advaitins bars women to indulge in the path of wisdom even in these modern days.  The orthodoxy is based on the experience of birth, life, death, and the world as a reality whereas the ultimate truth is based on the formless Soul, the Self.   Thus, Advaitic wisdom is for the whole universe irrespective of any gender, race, creed, and religion. 

Vedic women

In the Vedic era, women occupied a very important position, in fact, a superior position to, men. It is a culture whose only words for strength and power are feminine -"Shakti'' means "power'' and "strength.'' All male power comes from the feminine. Literary evidence suggests that kings and towns were destroyed because a single woman was wronged by the state.

The Rig Veda also refers to women engaged in warfare. One queen, Bispala is mentioned, and even as late a witness as Megasthenes (fifth century B.C. E.) mentions heavily armed women guards protecting Chandragupta's palace. 

In Vedic times women and men were equal as far as education and religion were concerned. Women participated in public sacrifices alongside men. One text mentions a female rishi Visvara. Some Vedic hymns are attributed to women such as Apala, the daughter of Atri, Ghosa, the daughter of Kaksivant, or Indrani, the wife of Indra. Apparently, in early Vedic times, women also received the sacred thread and could study the Vedas. 

The Haritasmrti mentions a class of women called Brahmavaadins who remained unmarried and spent their lives in study and ritual. Panini's distinction between acharya (a lady teacher) and acaryani (a teacher's wife), and Upadhyaya (a woman preceptor) and upadhyayani (a preceptor's wife) indicates that women at that time could not only be students but also teachers of sacred lore. He mentions the names of several noteworthy women scholars of the past such as Kathi, Kalapi, and Bahvici. The Upanishads refer to several women philosophers, who disputed with their male colleagues such as Vacaknavi, who challenged Yagnavalkya. 

 "India of the Vedas entertained a respect for women amounting to worship; a fact which we seem little to suspect in Europe when we accuse the extreme East of having denied the dignity of woman, and of having only made her an instrument of pleasure and of passive obedience." He also said: "What! here is a civilization, which you cannot deny to be older than your own, which places the woman on a level with the man and gives her an equal place in the family and in society.":~Santthosh Kumaar