Hum on car stereo when source powered by inverter
The hum is caused by  ground loop, a common issue with audio equipment that shares inputs with various devices within the same DC circuit (sometimes in more complex floating negative circuits too)

This hum is always there! It is just filtered out by the audio equipment using Ground as a reference point for removing this "noise", always.

This noise can include clicking from indicators(relays and high impedance), speed (caused by high voltage discharge on spark plugs) other mechanical/electrical related equipment.

The reason it starts to "pick up" this noise once you plug your charger into the inverter(which makes things worse because it "amplifies" all the noise) is that because the ground loops over the filtered audio and causes a double refernce which confuses the filters and assuemes this is the correct audio.

You need a simple ground loop isolotor between the inputs. or avoid creating ground loops. ie ( ground creates a full circle via the audio cable)



Just for fun

Professional (or highly addicted) car audio enthusiasts go to crazy extends in trying to reduce noise in audio to be able to amplify the signal into thousands of watts and over 120decidbels. Noise can cause speakers to distorts which technically makes the loudness go away and also damages the speakers core. Some methods include pre amplifiers, special and very expensive alternators-sometimes even several alternators that go through very expensive current stabilizers, and a variety of other highly priced goods. But unless you build something like this.. a simlple 3quid ground loop isolator is your best bet.