Is any open source software or Linux distribution engineered to the level of the 787?
Yes. Boeing Onboard Network System (ONS) running on the Network File Server (NFS)?
It and its 787 sibling are highly customized Linux distros.
Aircraft include the 747-8, 787, some 737, ...
http://www.b737.org.uk/flightinstsmax-maint.htm
https://www.teledynecontrols.com/en-us/Product%20Brochures/T...