In his weekly post-Shabbat class, Rav Yosef said that women who wrap themselves in a talit transgress Jewish law: “There are those Reform, they come to the Western Wall clad in a talit. They’re not performing a mitzvah, they’re transgressing, because of ['A woman must not wear men’s clothing, nor a man wear women’s clothing, for the Lord your God detests anyone who does this' (Deut. 22:5)].”Rav Yosef explained further that “Women are absolved of saying the Shma Israel – they needn’t make the blessing, much more so to wear a talit and make a blessing over it. A woman must not wear men’s clothing – if she puts them on, she transgresses. Women, even righteous ones, do not put it on.”
A 2001 Knesset law says that “no religious ceremony shall be held in the women’s section near the Western Wall that includes taking out a Torah scroll and reading from it, blowing the shofar, or wearing tallitot or tefillin. Violators shall be imprisoned for seven years.” But the law, as well as the 2004 Supreme Court decision that permitted women to pray as they wish at the Robinson Arch, next to the Kotel, did not refer to the actual wearing of talit as being contrary to Jewish law.
Rav Moshe Feinstein would side with Rav Ovadia’s opinion, based on his answer to the halachic inquiry (Igros Moshe – OC 4:49): “Can a woman wear a Talit? Answer: No. The Shulchan Aruch rules that it is Yuhara – religious arrogance (Shulchan Aruch, Orach Chaim 17:2). And if it is a Talit of men, there is a problem of Lo Tilbash – the prohibition of cross-dressing.” (source:ravaviner.com).
The Talmud (in Eruvin 96a) says that Michal, daughter of King Shaul and wife of King David, put on Tefillin. However, the Yerushalmi Talmud (B’rachot 2:3) says that the Sages objected to her practice.
As to the stories about Rashi’s daughters putting on teffilin, Ari Z. Zivotofsky, writing in the OU’s Jewish Action, suggests there is no evidence that Rashi’s daughters wore teffilin. Other sources say they may have, indeed, put on teffilin, but privately.