BTW-I haven't had much time to research the Amish perspective. Most sites seem to indicate everything is find. It just that it seems in the back of my mind a few years ago I read about problems. I'm not sure.
I don't remember a religious group. But ideas of secession, cultural or otherwise, are not uncommon.
There is a lot of thinking about making the South (sans Florida, it seems) a conservative stronghold. I vaguely recall someone, I believe by the name Michael Pierce calling us all under the flag of St. Andrew.
Walt Williams suggested Texiana to be formed from Texas and Louisiana.
There is a movement consisting of libertarians to resettle in one state, and move it in a libertarian direction. They are called Free State Project and they chose New Hampshire.
Problem is, most ideas of self-government come from libertarians, but they do not have a clear concept of moral law. How many Christian conservatives would like minimal taxation and no public schools if the community also legalizes drugs, gambling and prostitution, and won't do anything about abortion or gay "marriage"? How many libertarians would stomach localy enforced prohibitions on vice, adultery, or Sunday shopping? The two worldviews do not seem at all compatible.