The Rama says that a woman isn't allowed to put on Tefillin. The Magen Avraham that they aren't allowed to since "מפני שצריכין גוף נקי ונשים אינם זריזות להזהר" - "Tefillin require a clean body and they aren't careful".

What kind of cleanliness are we talking about. It's kind of hard to believe that woman (even 400 years ago) would go to the bathroom uncontrollably.

The Rama says (OC 38:3) that one must protest a woman's putting on Tefillin. The Magen Avraham there (sk 3) says that this is...:

מפני שצריכין גוף נקי ונשים אינם זריזות להזהר...
...because [Tefillin] require a clean body, and women aren't quick to be careful [about this].

What kind of cleanliness are we talking about? It's kind of hard to believe that women (even 400 years ago) would need to go to the bathroom uncontrollably.