Looks like the bug is that the shadows are not accounted for when
autoscaling. This is probably because of how the shadows are implemented
(iirc, they are an agg transform). The fix is probably to 1) add a bit of
padding when shadow=True or 2) make sure that clipping is turned off for
the polygons. (1) would work fine until it is time to use
bbox_inches='tight' as it probably wouldn't know about the shadows, while
(2) would look weird if one pans/zooms.

The reason the text looks fine is because they are explicitly set to have
clipping turned off, which would lend credence to having the shadow and the
pie polygons to have their clippings turned off as well.

Yes, and that's why set_clip_on(False) worked for me and solved the problem.

I'm fine with this solution, if you don't this is a bug in the lib which should be fixed later, feel free to close this report.

As long as the shadows are entirely inside the axes (which get_visible() should still return True on, even if all it's visible pieces are hidden) the pie-chart will be protected from the bbox_inchs='tight'.

It isn't an issue with auto-scaling, the axes limits are hard coded in axes.pie.