Basically the cowboy group does not want anything but soft cast lead bullets on their targets. For shooting paper use whatever you want minus tracers and incendiary stuff. I have a few of my own AR500 targets that I take out their all the time and shoot with jacketed bullets.
Even though the "copper washed" bullets are still essentially cast lead bullets, they are still prohibited for use against the soft steel metal targets on the cowboy range.
I usually have a washed bullet around on the dresser after a match. You know that last round you clear and winds up in your pocket and then goes through the wash.