I'm with Joe F...the temptation to sarcasm is great. This is because all music is acoustic. "Acoustic" should strictly mean "having to do with sound waves." Whether there is electricity involved in producing a sound wave has no bearing, in physics, on whether the wave is "acoustic."

There is a latter-day dichotomy between "acoustic" and "electric," two terms which never were opposites until very recently. Originally, it was not "music" that was defined as acoustic or electric, but the machines that produce music. The reason an electric guitar is only weakly acoustic, is that the guitar itself produces only very weak sound waves. The audible sound waves are produced outside the guitar itself, in an amp. But the music that comes out of the amp is no less acoustic for being electrically produced, and the resulting MUSIC is still acoustic, physically speaking.

What has happened is that the word "acoustic" has been taken from the realm of machinery (originally gramophones, and then guitars), where it meant "produces sound within the machine itself," (as opposed to transmitting vibrations electrically to a separate machine, which then produces the sound). The word has then been applied to the SOUND, which is pretty absurd. "Non-acoustic music" is like "colorless green" (or indeed "inorganic food"); it should be an oxymoron.

That said, non-electric music (which we now call acoustic) is a useful category to have. I think of it as a sort of ideal type: "acoustic" is one end of the spectrum and "electric" the other, and music is "acoustic" or "electric" to varying degrees. Music that is strictly non-electric would not be amplified at all, and cannot by definition be coming from a recording (unless it was recorded on an acoustic gramophone with a horn, diaphragm and needle). Music that is electric to a greater degree might be, for example, amplified or captured with the help of microphones, or might use a keyboard to emulate other instruments that are impractical to play. Music that is minimally acoustic (or mostly electric) would be music you could hardly hear if it weren't for the electricity (electric guitar or bass, etc.)

What this definition means is that you rarely ever encounter completely acoustic music in a professional context, and if you advocate for "acoustic music" you have to make your own decision as to what is an acceptable level of electricity. It's no good getting strict or pedantic, because you're usually not advocating complete purity yourself.