How much will the overall CMRR degrade due to impedance imbalance?
To calculate the system CMRR, you must evaluate the common mode to differential mode conversion that is occurring due to the mismatch of the + and - paths.

The signal amplitude at the output of each single ended half circuit is the impedance divider of the corresponding R and C. 

The reactance is X1 = X2 = 1 / (2*pi*50 Hz * 10 nF) = 354 kOhm.

We can then compute the voltage divider at V+ and V-.

V+ = Vcm * X1 / (X1 + R1) = Vcm * 0.9984

V- = Vcm * X2 / (X2 + R2) = Vcm * 0.9968

deltaV = V+ - V- = Vcm * (0.9984 - 0.9968)

To compute the CMRR, compute 20*log10(A_dm / A_cm)

CMRR = 20 log10 (1 / (0.9984 - 0.9968)) = 56 dB

For the differential gain, I'm assuming that the input resistance is large enough compared to 500 ohm that that input resistance voltage divider is approximately 1. If that's not true, you can refine the A_dm calculation.

This shows the importance of having well matched inputs when using differential amplifiers. This is especially true if external components are added to filter the incoming signal. You'll want to get the best tolerances you can get to avoid the common mode to differential mode conversion. Traces / cables should be matched to minimize the differences in source impedance and parasitics.

I'll mention a few other topics related to maximizing system CMRR. Keep inputs balanced and have low component tolerances as discussed above. This is about minimizing the mechanism by which common mode is converted to differential mode.

The next idea is to minimize the amplitude of the common mode signal. Your Vcm is presumably due to unwanted power line hum (50 Hz) coupling into the system. Isolating the circuit from earth ground will reduce the coupled power line current that can flow. If the interference is capacitively coupling into the system, you can look into shielding the input cables / traces. This provides a low impedance node for the interferer to couple to, reducing the effects on the signal. Twisted pairs for cables minimize loop area, which can reduce inductive coupling to the signal.

Additionally, there are architectures such as the Right Leg Drive (RLD) in ECG circuits where the common mode is sensed and an inverted current is driven back to the source to cancel out the common mode current. This is an effective way to improve the system CMRR. This may or may not be possible depending on your application.