There is an ancient tradition of women wrapping in tallit and donning tefillin, for they desire to fulfill the mitzva even if they are not obligated to - they want to do so out of closeness to Hashem. This is well known to us from the sources. Beginning in ancient times, through the Middle Ages and up to the New Age...
Also the haredim know very well that there is no prohibition involved, but the act seems to them to be provocative, and specifically because of that one must tread carefully between the action and the protest..
-- Rav Benny Lau
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