This is a complicated question. There are halachic grounds even within Orthodox Judaism permitting woman to wear a tallit and to read Torah in public. Needless to say, in Conservative, Reform, Recon etc. there is no question at all about this point. Yet there is also the concept of Shalom Bayit, one which I am expanding to mean peace among all of Israel. These women must have known their attempts to dawn a tallit and to read the Torah in public at the Wall would result in the current turmoil. Is this really helpful? I am inclined to believe that achieving equality within all branches of Judaism – and between all branches of Judaism – will not work with such divisive actions. In fact, it may achieve just the opposite. I suggests a more peaceful and conciliatory way needs to be found to achieve the rights Jewish woman do in fact deserve.
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from the article: Police arrest woman for wearing prayer shawl at Western Wall