What to do with GND of differential mode signals?
In general, yes you do need to connect a common ground between these modules.
The receiver hardware on the 'input' module will have a 'maximum common-mode' voltage spec for its inputs which you need to ensure is not exceeded,  and this voltage is measured with reference to ground.
Of you don't connect Ground between the 2 modules you don't know what this common-mode voltage will be potentially resulting in the receiving module incorrectly interpreting the differential signal and/or suffering some damage.