The 787 has this chip which has this back door, but the 787 does not have any ability to recieve reprogramming instructions into the FMC while airborne.
Data is transmitted to ground stations for monitoring purposes like ADS/CPDLC etc. but the FMCs do not acccept commands unless the cockpit crew choose to accept it. ie route loading, atc clearances etc.
The chips if hacked may corrupt the software logic of systems but the worst is a systemic shut down of automation.
Those familliar with Boeing system logic will see that when the auto mode is corrupted, it reverts back to primary basic mode; if the system continues to malfunction, the system is isolated!
So the threat may exist, but hackers bringing down a 787 is very isolated.
I agree the risk is very very remote but perhaps you under estimate how clever some hackers can be? To perform a hack on this type of system the person would need to be very familiar with the systems. That obviously makes much less likely to occur but also means any attack could be very sophisticated. We're talking about someone who might be quite capable of modifying a system (say while undergoing maintenance) in a way that is not readily apparent and which might fool other system into thinking it's working normally. These days the best hackers don't just shout "yahoo we're taking over", they are much too clever for that.
Perhaps worth remembering that two American space satellite systems were hacked in 2007/8...
Cover Story: Hacking Cases Draw Attention To Satcom Vulnerabilities | Defense News | defensenews.com
In the case of Landsat 7 and Terra, the hackers created highly specialized radio frequency signals and transmitted the signals to the spacecraft from the Svalbard ground station in Norway. They did so on four occasions in 2007 and 2008. The commission was most specific about the probing of Terra. On June 20, 2008, hackers “achieved all steps required to command” NASA’s Terra, “but did not issue commands,” the commission said.