We have a GE Spacemaker under the cabinet radio. Which has AM/FM/Weather radio, a CD player and an auxiliary input cable. It also has a incandescent light underneath with a high and low setting. I experimented with the light switch and noticed that if it is switched on or off with the radio playing on AM or FM there is a bit of a interference if you move the switch slowly. Sort of a slight popping or a squeak come over the speakers. However on Weather radio it isn't very noticable and on CD player or auxiliary mode, it doesn't do it.

I'm assuming this is because the switch somehow causes an interference with the AM/FM tuning, but somehow not on weather. Plus the CD and auxiliary don't utilize the tuner so it doesn't interfere there.

Another thing I've seen though, is if the cable is inserted into the headphone jack of my phone while the radio is playing AM or FM there is also a popping sound. Even though the phone isn't playing anything.

I know radios are often interfered by motors having brushes also, as well as TV, due to magnetic fields.

The switch causes broadband disturbance, most energetic at lower frequencies. So it is strong enough to disturb the AM.
The FM broadcast uses way wider bandwith (for sound fidelity), so even when on higher frequencies and more robust modulation, it picks up enough energy to be heard.
Weather broadcast uses FM as well, but it is on even higher frequencies (so less energy radiated there) and more important uses narrower bandwith (no need for any sound fidelity there). Thar means it captures way less from the switch spectra, below what is audible.