The name of the game is filtering and shielding. Okay names.
A metal enclosure would help. Putting an inductance in series with wires that pass into the enclosure help, and disc capacitors to ground from those wires also help.
Keeping a linear from interfering with an audio gadget can be simplified by filtering the power feed to the amplifier. A surprising amount of this kind of interference comes from an amplifier's hot and ground power wires. Without filtering, those wires become a transmitting antenna pumping a few Watts of RF into the immediate vicinity of the radio's mike. But high-current choke coils aren't cheap. Ferrite beads help, but the only way to find out if it helps enough is to try. How much filtering it takes to fix an issue like this is discovered only when the unwanted feedback stops. If a single snap-on bead to the amplifiers power lead is all it takes, great. And if you had to daisy-chain six of them onto the amplifier's hot wire, that's how you would find out.
73