Voltage divider on differential op-amp
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Va= 12V, Vin+=6V exceeds Vcm range thus output is saturated near  Vs=3.3V thus Vcm >= 3.3V is a violation and Vout saturated is outside linear range where output stays saturated with small changes of input which as we know if transfer function ΔVo/Vin= 0= gain is a violation of linear mode or "non-linear"

The 2nd example reduces the current sensor R-value to try to operate in the linear range.

other details

Although input impedances are mismatched 100 Ohms vs 100k, is a -60dB CM error comparable to 100k 0.1% error of also -60dB CM error per pair or -57dB worse case. 

This will never be as good as INA's with 120 dB CMRR at 10Hz. In both cases decreases by open loop gain at a closed-loop gain =1 .

The same is true for cables.  The impedance imbalance increases with frequency and 120 Ohm cables but they will never be as well matched as a DIFF AMP so the cable CMRR "can be" a problem resolved with very low source impedance and singe ended shields. For RF,  Baluns or Pi filters are also added to reject Vcm E-field noise on a long inductive cable at low f due to differential inductance error and induced currents.