An Odd Question

     Simple, just make sure nobody is playing any of them while listening and there will be no sonic impact.

That was easy,
      Tim

Wrong Tim. They resonate anyway. Not so easy after all.

I've never heard any notable change when I've had one of my acoustic guitars sitting on a stand as I played my stereo. True, sometimes the guitar boomed or buzzed a bit in sympathy but when it comes to tone or imaging emanating from the stereo, nothing. 

Sonic impact of having multiple (3) acoustic guitars on stands in your listening room?

To kill off most sympathetic resonances
Put a soft clamp across all the strings, and block off the sound hole in the bodies.

Cheers George

Yes there are sympathetic resonance issues, but unless you can actually hear them it's not an issue.  BTW, every object in your listening room is subject to sympathetic resonance.