Many guitar compressors have an EQ curve to them. When we tested the Keeley it had a slight mid hump and high and low fall aways. Some people say it sounds the most "natural" and doesn't change your tone. I'm sure it's a compensation for the way a compressor pushes down the guitar's midrangey hump, but in the end we went with a flatter frequency response for the Double Back.
Compressors absolutely change your tone. I'm not saying they act like multi-band compressors, but when you are above the threshold, the strongest frequency content is what drives the input sensor to squash down the signal. Then, there is recovery time. If we say your tonal content is comprised of the initial attack (crisp and trebly plus low end thump) the early envelope (upper midrange) and the decay (warm, less harmonic content, more fundamental) then a compressor can brick wall the attack, release slowly over the early envelope, and eventually add 20-60dB to the decay. That loosely translates into less mids and high mids, more highs and lows. Switch to a bridge JB for your guitar solo, and now it could totally emphasize the upper mids. Same with a Tele lead pickup.
Tone changes are the result of increasing the amplitude of certain frequencies, right? A compressor does exactly that, but dependent upon the frequencies contained in the source signal at the time of the squish or boost. If part of "
your tone is that "in your face" resonant peak of a pickup that sends your amp over the cliff when you dig in hard, the compressor will subdue it. If your amp has loose bass, a compressor can make it worse by woofing out your sustained notes.
To suggest a good compressor doesn't change your tone is really more of a studio thing. Once your track is recorded, and your tone has been achieved with your amp, cab, mics, etc. a good compressor will just control amplitude and you will not hear it as a tonal shift.