You start with a single ended signal from the sensor.
The sensor is grounded on one side, that's OK
The filter is for single-ended signals so that is OK as well.
Then you use a COAX cable which can only be used with single ended signals and that is what you do, so OK as well.
Now it gets a bit more tricky if there are (unwanted) signals flowing through the ground connection. The ground connection (COAX) will have some series resistance (all wires do) so any signal flowing there will add to the signal from the sensor (and there you have the reason for going fully differential).
Then you suddenly treat the signal as if it is differential because you feed it into a differential input amplifier. This is not wrong but also not OK.
But here you can probably get away with it since here the differential amplifier circuit will simply see a "wrong" differential signal since the bottom input is grounded. The amplifier will look at the difference between the inputs and that is equal to your signal. So this will work.
But with this you do lose the benefit of differential signals and that is the suppression of (common mode) disturbances. However, you are using a COAX cable which shields against these disturbances.
Connected like this the differential amplifier cannot even filter out the common mode signal because the signal is not differential!
Also if you want to use a proper differential setup then you have to:
add a single to differential converter circuit after the filter
replace the COAX cable with a 3-conductor cable (2 signals + 1 ground, the ground and shield could be the same).
In a fully differential solution the only currents flowing through the signal cables are the signals themselves. A current through the ground cable is no issue as it will not add to the signal.