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I've seen public schools posted with 30.06, though they don't have to. It's still illegal.

I'm not sure where I acquired the concept, but somewhere I picked up the definition that a 'school' is an elementary or secondary education institution that receives federal education funds (as well as property tax revenues from the area it serves).
You local ISD's elementaries would be 'schools'. Karol's Kiddie Kollege (daycare funded entirely by fees charged to parents who leave their kids there) would not be a 'school'. A daycare or pre-k that is in the Headstart Program would be a 'school'. A state-funded junior college would be a 'school'. Joe's Barber College would not (unless it was receiving federal job training funds).
Sunday School would not be a 'school'. Sunday School in a church run orphanage that receives some federal funding might be a school.

Even if it's accurate, this definition probably confuses things more than it helps.