The absolute no no would be running ethernet next to power cables. Anything digital next to power cables is a big no no. I would still not run analog by power, however.
Running ethernet next to speaker cable isn't likely going to do anything. However, there is still a magnetic field around the speaker cable when it's being used to drive a loudspeaker (and the music is playing, the amp is pushing volts and amps.) If you had a very high end system, it might. My system is ultra reveling and I try to space out absolutely all cables. If they have to cross, try and cross the cables at 90 degrees to each other. If you have no option but to keep them together, it won't make or break anything. As long as your not OCD, haha.