In Murphy, North Carolina, a peaceful mountain town once defined by birdsong and swaying trees, a steady electric hum cuts through the calm. The noise from a nearby cryptocurrency mine has intruded on Rebecca and Tom Lash’s lives since it opened in 2021.

“There was nothing in this little pasture but these electric lines,” Rebecca Lash said, as she and Tom stood on the hill overlooking the mine. “And it was just nice and quiet.”

The Lashes came to Cherokee County eight years ago to settle down and enjoy their older age in view of the Blue Ridge Mountains. They grew more…