Hello Alex,
Likely you're running a signal flow similar to this one:
I tried it on a stock Eval-ADAU1701Miniz board and could not duplicate your issue -- a logic Low at the MP2 pin completely muted the sound. This result makes sense because the DSP volume control, unlike a voltage-controlled amplifier or similar form of analog volume control, works perfectly. It multiplies its control input times its audio input, and zero times anything is zero. By contrast the -1701's ADCs and DACs are not perfect, but with THD+N better than -83 dB, and S/N of 100 dB. You can compare your measurements with these specs.
Here's a suggested test for your application: Make a copy of your SigmaStudio project and modify the copy as shown below:
Obviously, no input sound should reach the output in this program. Load the modified project and listen. If you hear the same weak, distorted sound as before, then its cause is not the volume controls letting audio through, but rather, another cause within the hardware. Possibly a ground loop.
Output gain in itself is not a problem (and would be present in any practical system driving speakers). The ADAU1701's inputs are fine with higher-value resistors to scale larger inputs. Where I work we protect the ADC inputs with back-biased diodes to the 3.3 V and ground rails, I've also seen this recommended on the forum.
Best regards,
Bob