What are the consequences of women chanting mantras? Do scriptures say anything about this?
Let me share with you some of my findings.
Find 1.:The 108 names of Skanda(Karthikeya) given by Maharshi Viswamitra is found in the Skanda Puranam.Refer to the Phalasruti(of reading the Ashtottara Stotram) given below.
Sage Viswamitra recited the following Ashtottara Namavali (108 names) about Skanda Deva on the most significant day of Kartika Pournami of which Kartikaya is fond of:...
Phalasruti: Those who recite the Ashtottara of Kartikeya become fearless, contented, and happy; a pregnant woman reads or hears the Ashtottara would be blessed with a son of virtue and fortune; and if unmarried girls read they are sure to secure ideal husbands.
Find 2. Refer to the Phalasruti of the Brahma Vaivarta Puranam as found on this page:
....It demolishes of Vighnas (obstacles of any kind) and yields fruits of performing Yagnas, Tirtha Darshanas, Vratas and Tapasya. There is no exaggeration in saying that reading this Purana excels �Veda Pathana�. Any unfortunate woman reading this would result in prosperity to herself and her husband. The Purana Shravana or Pathana blesses the person concerned with good progeny, good wife / husband, and name and fame. It relieves of diseases to the diseased, shackles from imprisonment, dangers from the victims of great risks, and panic to those experiencing fright etc.
Find 3: From this chapter of the Brahma Vaivarta Purana
-Devi Savitri is the mother of Vedas whom Brahma Deva worshipped first followed by all the Devas. A reputed King of Madradesha called Ashwapati and his queen Malati whose qualities of virtue, charity and devotion brought them fame in the contemporary times but had unfortunately no children. Maharshi Vasishta gave �Upadesha� (Instruction) of Gayatri Mantra and the royal couple performed sincere �japa� (repetitive muttering of Mantra) and worship but to no avail; they shifted to Pushkara Kshetra and intensified their devotion.
So,it seems women are allowed to recite Mantras,Scriptures etc.
As & when i find more relevant references i'll keep updating my answer with them.