I've heard and seen religious Jews painting the backs of the tefillin straps black, and they claim a kabbalistic reason somewhere in the Schulchan Auruch. Does anyone know anything about this, the reason, and source?
There are opinions that this makes the Tefillin a more beautiful Mitzvah. Although the Arizal may be one of them, the Rambam, the Or Zarua and others who are not regarded as kabbalistic in their rulings also rule this way.
The general custom is to not do this, but as you noted, there are those who follow those opinions. Nobody puts it as a requirement (except perhaps some Kabbalists, depending on their understanding of the Arizal), but rather as a Hiddur Mitzvah.