I'm sitting here playing my guitar when all of a sudden I hear a guy and woman talking and I realize it's coming from my amp, picking up a radio signal just like how a cordless phone would. Is this a common thing?

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its common with anything that has a speaker and receiver. I remember being in jr high school and sitting in iss top floor, and hear people order Bojangles food from the intercom located in the room.

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What type of amp do you have(tube/ss/hybrid), how old is it, do you use a noisegate, high quality cables? Using good pickups? Tried it with more than 1 guitar?

I'm having the same exact issue with my Engl but I figured out what it is by running a multi FX pedal straight into the FX loop return of the amp, skipping the amp's preamp. The radio signals in my case are being picked up by the cheap stock preamp tubes it has, so I ordered some recently. If you have a modeler like a podxt/v-amp pro or a multiFX pedal laying around, plug your guitar into it and plug it into the fx loop return of your amp and see if you still get radio signals.

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