Actually, thinking about it, Wobble could be right with the Plymouth or Exclusive Brethren example.
There are not insignificant numbers of the Brethren still operating but they concentrate on their born ins and keep the rest of the world at arms length. They are suspicious of technology and are happy to lobby political groups to support social issues that fit their world view. they are isolated and introspective and they practice shunning at least as ferociously as Jw's.
As the GB struggle to deal with the proliferation of information and opinion they may well start to retrench and concentrate on keeping the born-ins in. They will spin this as the 'closing of the door to the ark'. Too bad if you're not inside.
They will continue to shrink in numbers and their clothing styles will begin to date them.The women will start to wear scarves all the time and some weird genetic thing will happen from all the marriages taking place inside the group, you know, something like half the kids will be ginger and speak with a lisp.