Intel GPUs require neither a blob nor reverse engineering, so ironically the Minnowboard (http://wiki.minnowboard.org/MinnowBoard_Wiki_Home; current revision is "Minnowboard Turbot") is very open (also the UEFI implementation (TianaCore) is open source; just a small FSP (Firmware Support Package) by Intel containing binary data has to be compiled in - as far as I know it contains no suspicious data; start at https://firmware.intel.com/projects/minnowboard-max if you want to read about the details). I am rather sure this processor/board has no support for the dreaded Intel AMT.
If you want an ARM board: The "Sabre Lite - i.MX6 Quad Core" board is the nearest to this ideal that I know of. Traditionally Freescale has been very open with the specifications (though after NXP bought them this changed to worse). The GPU (Vivante™ GC2000) is not strictly in the category "No binary blobs, no reverse engineering", but I have read that this is among the GPUs found on ARM boards by far the most easy one to reverse engineer, thus there seems to exist a decent reverse-engineered driver:
> https://en.wikipedia.org/w/index.php?title=Free_and_open-sou...
(EDIT: For the situation for open Vivante drivers also see https://www.phoronix.com/scan.php?page=news_item&px=Etnaviv-... (from https://news.ycombinator.com/item?id=12743550)).