The Talmud indicates that the logic here behind the sages not objecting is that it is a woman’s right to do a mitzvah which she is not commanded to do. I don’t see where guf naki is inherent anywhere in that gemara.
The Hagahot Maimoniyot says that Bavli says that Hakhamim did not object to women who performed Mitzvot such as Tefilin and Aliyah l’Regel, and that he heard that we protest only where there is concern for transgression, such as with hullin be zarah or ervah.
My understanding of Tosafot is like this: Rashi says that if it were Zeman Gerama, hakhamim would have protested due to Bal Tosif. The Ri disagrees. R. Yehudah holds that Ein Nashim Somchot Reshut, and he holds that Hilni ha’Malkah used to sit in a Sukah with her sons (Sukah 2b)! However, perhaps she sat due to her sons, so it does not look like Bal Tosif. Alternatively, Rava holds that not at the time of the Mitzvah, one transgresses Bal Tosif only with intent. A woman is exempt, so it is considered not at the time of the Mitzvah. However, this is difficult. Rather, the one who holds that it is Zeman Gerama forbids women because they are not careful enough to have a clean body like Tefillin requires. Olat Re’iyah looks like Hullin ba’Azarah, or entering the Azharah without need. Blowing a Shofar is a Melakha mi de Rabbanan.
Ran (Rosh HaShanah 9b) says that we’re not concerned for shevut or baal tosif by women doing MASZG.
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