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:
The K1 chip has a blob-free boot (unlike the newer chips AFAIK) except for the USB-based flash programming / recovery mode, so for the initial installation you'd need to manually flash the eMMC somehow if you don't want to run any proprietary code.
And yes, CUDA isn't supported by the open drivers. Other than that, I've heard Nouveau works relatively well. Though I'm not still sure if the open source graphics community has figured out a way to get stacks like Xorg or Wayland/Weston running without hacking the source on architectures where rendering and scanout are done by different DRM devices.
1. A GPU
2. No binary blobs, no reverse engineering?