The Rambam says in MN that animal korbanot were instituted as a concession to pagan influences and people’s tayva towards that back then. Rav Kook thought that in the Messianic era, there would be no animal korbanot.
For those who hold like the Rambam, Talmudic gezerot are binding even when the reason for then is no longer applicable, whereas the Ryevid feels that such gezerot are no longer binding if the original reason for them is no longer applicable. Tosafot is inclined towards that view, as well.
Regarding women and tefillin: Tosafot there suggest that women are incapable of maintaining a guf naki. This wasn’t a concern to Rambam, who simply allows a woman to partake of any mitzvah she desires, even if she’s not commanded to do so. Nor did it seem to have been of concern to Hazal in their allowing Michal to wear tefillin. My one caveat would be that women who engage in wrapping tefillin should not say the berakha. I have a friend who composed alternative texts for women to use when wrapping tefillin and putting on tallet and tzitzit. The same friend also composed very appropriate texts for calling people up to the Torah minus a minyan (while this is intended for WPG’s, I have made use of it in contexts where there was a sefer torah and no minyan on yom tov mornings and some shabbatot where I lein, as we sometimes can’t get a minyan).
Tosafot cites guf naki, which later rabbis cite as a reason why men don’t wear tefillin all day long, ironically.
I’m not big on labels. Judaism is either halakhic or it isn’t. Denominations don’t lead us to a place of greater halakhic observance, as their are many things contra halakha that are done in the Orthodox world. The problem with Conservative is that they singlehandedly decided to assume that they have authority to permit what goes against Oral Torah Judaism, and subsequently, they have a huge dearth of committed membership. Anyone who was traditional and part of JTS is now generally accepted in the MO camp, such as Rabbi Alan Yuter, or Rabbi David Weiss haLivni.