How to mitigate an unavoidable ground loop in a vehicle?
If it's automotive, consider EMI for your solution as you likely need it qualified.
You have to prevent a large loop between battery positive, display PCB, LDO, sensor PCB, sensor, chassis, back to battery negative.
This happens if you cut the chassis bond of the display board, although it will solve the ground loop. The large loop will remain and cause a lot of stray radiation pickup and voltage spikes in your circuit.
I can think of two solutions instead:
Option 1:
Use an isolated 12-&gt;5V converter to create power for the sensor and run the power and data lines each through common mode chokes over to the sensor. Ground the isolated sensor power negative on the sensor board and leave it float on the display board (cap-attach it to the display ground as per dc/dc converter design rules). Bond the chassis, to both boards and the the cable shield on both sides.
To power the display board, you must not use the isolated sensor power. You can use a local non-isolated psu for that (e.g. your LDO).
Option 2:
This is without an extra PSU, so potentially lower cost. It is also a variation of Bruce's answer. Remove the 12 V connection from the Display Board, and feed 12V power into the sensor board instead. Pass this 12V and a return wire (with Common mode choke) through the cable to the display board's LDO.
In this case, too, keep both boards' end of the shield attached to local chassis. But the Display Board's ground must not be DC-bonded to chassis. Only RF-bonded.