You may have an ignition switch issue due to cylinder wear and/or key wear. What may be happening is the ignition cylinder is still turned slightly from "OFF".
Normally, there wouldn't be a ding if the keys were out and the truck was off when you open the door. If the key was still in (OFF) or vehicle running, driver's door open will chime, passenger door will not. When you shut the door, key in off or vehicle running, chime will stop.
Next time you're in the truck and it's running, see if you can wiggle the key out of the ignition. This is the sure sign of cylinder and/or key wear.
'01 XLT disguised as a '03 Fx4 Level II
Big. Loud. Slow. Bright.