Why does noise gain matter more for stability?
The noise gain is what determines where the fixed gain line intercepts the gain-frequency line on the Bode plot. The noise gain line needs to intercept the Bode plot above the point where the phase margin goes to zero, and ideally above 45 degrees for limited ringing to step signals. The noise gain is the same as the signal gain for the non-inverting configuration (signal connected to + input. It is equal to the signal gain plus 1 for the inverting configuration (+ input grounded, and signal connected through a resistor network to negative input).