The problem lies with whats called a Ground loop. The radio, for lack of a better term, is using the speakers as a ground.
Pull the radio. If you used an adapter pigtail, make sure you Solder the power and ground leads.
Check the ground wire size, make sure its same as power. Check the ground wire ( truck off, key out) coming to the radio, to truck ground with a ohm meter. I turn on the beep on my meter, so I don't have to look at the resistance.
Probably a NEW ground wire from the chassis of the radio, to a GOOD truck ground, ( possibly one of the 2 cigar /12 volt outlets below) will do the trick. Good luck!