Amish et al.

How do separatist anachronistic religious groups like the Amish or Ultra-Orthodox Jews manage to educate their children in a way that conforms to state and federal requirements?

First hand experience here.

Where I grew up in Western PA, the Amish moved in and established a community to the north of us. They simply did not believe in education past the 8th grade level, and PA law allowed kids to be pulled from school on a “farm work permit” at age 14. Typically, they build their own schoolhouses which provide basic education to that level, and which meet with requirements well enough to satisfy regulations. The first few years they were there, they rode the buses into the public school (they can’t own or operate motor vehicles, but they may ride in one operated by the “English”). They pulled the kids at 14 on the aforementioned permits, and in a couple years had built their own school. My mother taught juniour high (this was before they called it “middle school”), and mentioned something curious - the Amish kids were often discipline problems. They knew they were out at 14, and also knew that they were going to have precious little chance to get off the farm in the future.

Look for the case Wisconsin vs. Yoder. Kinda interesting.