In the application identified by the TS as a musical device, exact repeatability is certainly not a requirement. Mostly without exceptions musical instruments are played by ear to some extent. That is why there are no deaf violinists. Certainly the force dependent resistor is not suitable for an accurate scale to measure weights precisely, but it will be totally satisfactory for "louder" and "softer" control where the operator is in the feedback loop. Using the right tool for the job, or in this case, using the correct component for the job.

What is the difference between if the sensor is in the feedback loop (as in the schematic provided) or if it dictates the voltage at the non-inverting input, as in this schematic? Is one preferred?

 

What is the difference between if the sensor is in the feedback loop (as in the schematic provided) or if it dictates the voltage at the non-inverting input, as in this schematic? Is one preferred?

As the moving tap on the resistor moves from common to V+ the output voltage will vary in the opposite directions. That is because one feeds the inverting input while the other feeds the NON-inverting input.