Reb Moshe clearly opposes use of a talis by a woman because the Rema calls it arrogance.
Igros Moshe, Orach Chaim 4:49:
“In regard to the women who participate in the battle [feminism] with other women of the world. These women who are Torah observant wish to bring this battle to the arena of Torah law and therefore some pray with Talis and Tefillin and the like. They wish that I state my opinion on the matter. However, it is obvious if her soul desires to fulfill commandments which she has not been commanded. However, since this is not the motivation, but rather due to her complaint against G-d and His Torah, this is not a Mitvza, on the contrary, it is a sin.”