How can you evaluate a system with highly processed music?

You can not. You must use a “known sound”.. unprocessed acoustical to calibrate your system, then you can be sure that electronically and processed music is being reproduced with equal fidelity. 
 

For almost 50 years, I know what certain instruments sounds like because I have them or my band members had them. Sure a Marshall amp sounds different than a fender tube amp, a Rickenbacker sounds different than a Stratocaster or a Les Paul, and a zildjian sounds different than a Sabian (same size/type of course).

From the 70’s, I would take albums into stores with my favorite music that emphasized certain instruments and I would make most of my decision on how the system recreates that sound. Once it passes the 1st phase, then on to the other criteria. But if an instrument doesn’t sound like the real thing which I have access to, then it’s a waste of time to go forward with this gear
 

John Atkinson made the point to Gordon Holt that the sound made by an electric guitar plugged into an amplifier was just as much an acoustic signal as is an acoustic instrument, and he was correct. But recorded sounds produced purely electronically is a different matter: that sound never traveled though air, from an instrument (whether acoustic or amplified) to the recording microphone. There are plenty of recordings in which the electric bass, electric guitar, and/or keyboard instrument/s was/were plugged into the recording console, not into an amplifier and then recorded with a mic.

I’ve watched and listened as a recording engineer played with the dial on a studio’s parametric equalizer (far different from a graphic equalizer), drastically changing the sound of the recording. For evaluating the timbral neutrality of loudspeakers, make and use your own recordings! Listening purely for pleasure is a different activity. "Turn off your mind, relax, and float downstream" as someone once sang. ;-)

@mglik not sure if you have read this old piece.

https://www.stereophile.com/content/capturing-it-live-peter-mcgrath

I was lucky enough to listen one of Peter's recordings recently. Needless to say I almost got tears in my eyes. I'm now also considering upgrading to the Alexia V.

The performance and arrangement are certainly most important.

I do, however, most enjoy acoustic instruments and voices.

Heavily processed Pop, etc. can surely be a lot of fun. And the performance of my system can also be evaluated with any content. 
However, I believe acoustic instruments and vocals are able to be a gauge.