Sounds like it’s all in their heads, but the stress induced by worry can cause real illness.
The meters, with transmitters, can be easily shielded.
Take one of those very large cans, the really big ones that hold tomatoes found at COSTCO, and cut it in half from top to bottom. Mount it behind the meter/tranmitter between house and meter.
There you go, all assured of a good night’s sleep without those nasty radio waves.