I replaced the factory Rockford Fosgate 6 disk changer with a Rockford
Fosgate RAVDVD1 head unit in a Nissan Xterra with the factory Rockford
Fosgate 300 Watt amp. I hear a loud thump (pop) from the speakers when
I change radio presets, or switch from tuner to CD mode. I also hear
the thump when I turn off the ignition (but not if I turn off the head
unit first).

I have done quite a bit of experimentation, including looking at the
head unit outputs on an oscilloscope for both the factory head and the
RAVDVD1. The difference/cause of the thump is that the RAVDVD1 drops
the DC portion of its output when the unit is quiet (switching
presets, modes, etc), whereby the factory unit leaves the DC portion
high during these times.

Is the problem is the AMP's behavior or the new head unit's behavior?