Alpine HU replaced BOSE stereo

This is not a problem with Alpine, it's a problem with fitting any aftermarket HU to the Bose system using the RCA outputs as the feed to the Bose amp. Bose (and non Bose) use a wierd capacitor input stage to their amps which is not industry standard. Alpine and any other brand will mute/ground the RCA's when doing anything electrically noisey like changing CD, switching on/off etc. This effectively discharges very quickly the capacitors on the input stage to the amp which results in the popping.
The only way round it is to use the speaker input adapter (rather than the RCA input you currently have). Not ideal as it uses a line out converter to take the amplified speaker output from the Alpine back down to pre-out level, only then to be amplified back up again by the Bose amp.
Seriously you'd be far better off removing all traces of the Bose system including the speakers and driving everything off the Alpine. You can't drive the Bose speakers off the Alpine as they are 2 ohm impedance, but they are not the best speakers in the world anyway. If you don't fancy replacng the speakers then replace the Bose amp for a 4ch unit that is stable at 2ohm.

As AndyMac says ditching the Bose stuff is your best option, but rich_dj used capacitors on the RCA output to overcome his similar problem description 18th post down.

http://www.audi-sport.net/vb/showthread.php?t=26307

It's in the righthand cubbyhole sandwiched between the back of the rear lights and the wheelarch.