we still have people that do not believe that the phones are always listening when seemingly any website or app you use gives you advertisements about what you were just talking about in the other room with the phone locked.

Oh come on. Don’t bring this into conspiracy territory. Yes, eavesdropping does happen, but it’s not something an uncompromised Android phone will do when locked. Even when it does happen in the case of spyware, the people doing it aren’t selling your transcriptions to advertisers.

People should still opt out of as many of GAPS’s spyware-like features as possible, as you suggest, but not because it’s a special anti-listening-device warding spell.