This project and coreboot seem to me, complimentary. It is already possible to run TianoCore over coreboot, it seems it should be possible to run Mu with it as well given some work.
Disclaimer: I do work for MSFT but never on UEFI - this is an outside observation
If Project Mu requires UEFI, then you'd need coreboot+TianoCore+Mu. In theory contributing to coreboot would have been far more useful, but their idea of being able to easily update firmware would work better on UEFI. Coreboot does allow easy flashing by default but it's not really meant to be enabled on user systems (since it allows for "firmkits").
Disclaimer: I do work for MSFT but never on UEFI - this is an outside observation