Rav Yosef suggests that men and women are treated as separate categories, therefore something which qualifies as a tachshit for a man and permitted to be worn on shabbos will not be a tachshit for a woman, unless it is also normal for her to wear that type of item. The gemara asks from a Braisa which permits a woman to wear tefillin in from the reshus harabim on shabbos. The assumption is that tefillin is a time bound mitzvah from which women are exempt. Therefore, if we assume that "women are a nation unto themselves" and what qualifies as a tachshit for a man doesn't impact a woman, it should be forbidden for a woman to wear tefillin on shabbos because it should be considered carrying? The gemara responds by saying that the author of the braisa holds that one is obligated to wear tefillin both at night and on Shabbos making tefillin a mitzvah that is not time bound. Since women are obligated as much as men, it is considered a tachshit for women also.
There is a very serious question that can be asked on this gemara. There is a machlokes between Rabbeinu Tam and the Rambam whether or not women can make a bracha on time-bound mitzvos, but all agree that she receives reward for fulfilling these mitzvos as an אינה מצווה ועושה. Being that a woman receives reward for wearing tefillin, how can we consider her wearing tefillin to be an act of carrying? However, if we ask the question as simply as we just did, the answer is obvious. Although women get a mitzvah for wearing tefillin, we are speaking about shabbos for which there is no mitzvah to wear tefillin. Therefore, for a man who wears tefillin during the week it is considered a tachshit even on Shabbos when there is no mitzvah (as the ritva explains on the gemara 61a) but for a woman who isn't wearing tefillin during the week, since on Shabbos there is no mitzvah to wear tefillin, it is not considered a tachshit for her. If we take this approach, it should follow that if shabbos would be a time for tefillin and women would be doing a mitzvah by wearing tefillin on shabbos, it should be permitted for them to wear tefillin, even if they aren't wearing tefillin during the week. If this were true, the gemara should have simply answered that the Braisa holds that Shabbos is z'man tefillin, so that even if night is not a time for wearing tefillin making tefillin a time-bound mitzvah, they can still wear tefillin on Shabbos since by wearing it they are fulfilling a mitzvah. Why does the gemara feel compelled to say that both night time and shabbos are a zman tefillin and transform the entire mitzvah into a non time-bound mitzvah, as Rashi explains. It should have been able to justify the women wearing tefillin without having to go to such an extreme?
From the fact that the gemara goes to the extreme that it does, it implies that the only justification to permit women to wear tefillin in reshus harabim on shabbos is if they are exactly equal to men in the obligation of tefillin, but by simply being able to perform a mitzvah by wearing tefillin on shabbos wouldn't justify the right of a woman to wear tefillin. Why?
I found that Rav Moshe (Dibros Moshe, Siman 50, anaf 4, pg. 336) addresses this issue. At first he suggests that based on Rashi in Eruvin 96 who considers women performing time-bound mitzvos to be bal tosif, and even Tosafos who at least when it comes to the mitzvah of tefillin considers it inappropriate for woman to wear since it is hard to maintain the proper level of cleanliness, we can explain our gemara. Since women are not supposed to perform this mitzvah, it isn't considered a kiyum mitzvah for them to wear tefillin on shabbos even if shabbos is a z'man tefillin. Therefore, the gemara is forced to say that women are fully obligated in this mitzvah. However, Rav Moshe suggests that if the gemara was asking from the perspective of issur rather than p'tur, it should have said so explicitly and also should have cited some proof that there is indeed an issur. Therefore he suggests that even if women would be fulfilling a mitzvah by wearing tefillin on shabbos, this would not justify their ability to wear tefillin in the public domain. The rules of what is considered a tachshit or malbush is very practical. If women have the practice to generally wear tefillin, it would be regarded as a tachshit, but if they don't have that practice, even if they would be performing a mitzvah by doing so, it is not considered a tachshit. Therefore, the only justification to allow a woman to wear tefillin on shabbos is to change the nature of the mitzvah to be a non time-bound mitzvah making women completely equal to men in this mitzvah.