I found the circuit to be quite sensitive to external disturbances and noise, so shielding everything is a very good idea. Here's a plot of a 4µVp-p 10-minute-period square wave injected directly into the HX711 channel #1 inputs with gain=128:

The measurement is in ADC counts. The input resistance was 10kΩ, so the 1µF input capacitor formed a 16Hz corner frequency. (At this point you should be asking yourself, "How did he inject a 4uV signal with a common mode offset of 1.65V?") The software can easily measure mean and standard deviation, so I estimate that the input referred noise is about 500nV p-p. That is on par with other amateur ADC systems designed for velocity sensors -- and compares favorably with ADC systems costing 100x more.