When a stereo pops with the switching of other components, it can usually be traced to a problem that has arisen from a compromised ground plane... Isolation transformers can work to minimize or eliminate the pop from the stereo, but know it is a bandaid and not a fix. The pop is still there, but the filter hides it from the stereo.
Maine is right in his assesment... Check all grounds. I will add the following:
Rather than buying noise suppressors that only mask the problem, the better practice will be to try track down the exact event that caused your popping to start. To your point about it affecting the stereo regardless of source; this definitely points to a power wiring problem. Know that other electronics can be affected negatively; you notice it in the stereo only because you can hear the stereo. It will be better to get rid of the pop with a solid step-by-step diagnosis... Better for all of your electronics
A few suggestions:
* A radio will often power up even if it is only grounded through the antenna lead. disconnect the AM/FM antenna and see if the radio quits. If so you have disconnected the primary ground wire somewhere or somehow. Find your open on your radio ground wire and reconnect it.
* Check to make sure the Shield conductor of your antenna wiring is not accidentally shorted to another ground that leads to the battery. This shorting will create two paths to ground with a voltage potential difference in the ground path that will allow the dual ground plane to act like an antenna.
*Make sure the case of the radio is not accidentally touching any other wire, be it ground, antenna, power, speaker or other. The metal case is often completely disconnected from the internal electronics and is there to act like a Farraday Cage. If a wire is touching it, the shielding will be compromised.
* Is there any lighting in the switched circuit the stereo lives on? An accidentally series-wired light bulb will show zero resistance at meter voltages, but is a voltage drop at the current a radio lives on. Make sure youy are parallel wired straight to the battery or power distribution point.
* What prompted you to be tugging around on the wiring behind the radio? This often is a result of adding electronics. You sure you did not add any offending electronics?
* Re-check and remove and replace any power wire terminations or connections behind the radio, (red, yellow and black). You might have had corrosion that was slowly creeping up on ya, and the movement of the wiring was the straw that broke the camels back. A good looking connection might still be a poor electrical connection.
*Check other electrical devices in the boat for weakened connections and loose, missing, or dual grounds.
*Check to make sure your battery is charged and connections are good. Low voltage is a prime cause of stereo noises and pops and it can be often fixed with a wrench or twist of a wing nut.
The situation did not exist previously, so a power filter or other isolation transformer device is a patch, not a fix... Go find the problem and you probably find that the stereo AND the other gear works better....