You are playing a joke on us, right??
The two systems are only connected electrically and maybe communicate on the CANbus. One shouldn’t have any effect on the other, in theory. I’ll give this some thought and return. Maybe someone else here has heard or seen this problem.
The daily stumper!
Edit: OK, did a search and found this isn’t all that uncommon and the ignition switch is often the culprit on GM vehicles. Apparently they are less than a $100 for the switch alone.