That's actually a bad control group; you want some group whose lifestyle, including lifestyle changes, matches pretty well the rest of society but for exposure to the kind of radiating devices at issue, to isolate changes due to the effects of the devices at issue from the effects of other lifestyle changes.

Since the Amish lifestyle and lifestyle changes over the time period of interest don't match the general public in ways other than cellphone/wifi exposure, they aren't really a good control.

The Amish live in a very different environment from the general population in all sorts of ways. So they're not a good control group, because where their health differs from the general population, you don't know if it's because of radiation exposure, diet, electric lighting, chemicals in cars, or any of a thousand other things.

The Amish are a bad control group because they have a very small gene pool among other reasons.