If a woman finds a tallis or tefillin in the reshus harabbim on Shabbos, what should she do?
Is she allowed to put them on and walk to a place where she can then take them off and put them down safely?
The Mishnah Berurah (301:158) cites a dispute concerning this matter. According to the Magen Avraham a woman must not wear Tefillin, and this is considered a “load” on Shabbos (because it is not considered a garment for women).
However, the Shaar Ha-Melech (as cited in the Mishnah Berurah) writes that this matter is the subject of a dispute between the Rashba and the Raavad. In practice, the Rashba agrees to the Raavad that women should not wear Tefillin.
However, it is possible that concerning a Tallis all agree that a woman can and should wear the Tallis — though even here the Magen Avraham writes that it is forbidden. The reason for the possible distinction is that for Tefillin there some halachic foundation for women not wearing Tefillin, whereas this doesn’t apply to a Tallis.