Funny you posted this I have the same issue. Thought it was just USB drive, then tried blue tooth and it does the same with no music playing or when a song is paused etc... It's not much but it's there. I'm grounded to battery on the amp, made sure speaker wires weren't anywhere near touching power cable, even using the wire separator on the kicker marines specially to stop any interference. I'm thinking it's related to how I'm using ride command single left/right audio signal vs a real head unit. Sounds good when music on though, so not sure I'm motivated enough to buy a new radio and give up ride command yet lol. Curious what you find out if you do take it in!
I had that problem about twenty years ago with an amplifier that I installed in a Dodge Caravan. The system sounded terrific until you started the engine and then the whine would ruin everything. If I remember correctly, I used an inline noise filter designed for that very type of problem and it worked. I suggest trying that before you throw in the towel on the Ride Command.