Hi @RWB
If you are careful with the power connections for the optoisolators, then yes they will get you out of ground problems. So in your schematics above, exactly which +5 and which GND you are using is key. If the GND pins on the two sides of the optoisolator are not connected together, that will work OK but your schematic does not indicate that.
Turning off serial makes all the pins be high impedance inputs (with protection diodes) so that can possibly open a ground problem. A no-ground situation can cause inputs to float and work at some times and not others as well.
Your scope also has a hard ground which is typically connected from the probe to earth safety ground. This is normally a good thing for your safety but there are times when you must run a scope without a safety ground on a isolation transformer. I have seen cases where the scope probe ground wire acted like a fuse and melted due to high current.
I am not saying that your problem was absolutely a ground problem; I’m just saying that your strange symptoms do fit that hypothesis. If you don’t know for sure how the systems are grounded, you could poke around a bit with your scope and likely find out. Try connecting the scope probe tip and only the tip to one system’s GND pin and see if there is DC there. Look at the other pins relative to earth ground too. Then try the other system.