BeagleBone Black is actually quite good about freedom. Of all the ARM
development boards out there, BBB is one of the only ones that you can
reasonably run using entirely free software.
The only component on the "Beagle Core" (and BBB for that matter) that can't
be run using free software is the HDMI chip... however you can disable that
in the device tree, and especially for a board like this you probably don't
need HDMI or video encoding. This seems like a great platform if you can get
away with running it headless over a network or serial connection.
You could, for example, flash Libreboot onto a thinkpad using this device
with only free software (though would probably be easier to do it with a
regular BBB for that particular application).