As I work at in a university environment, what we theatre faculty and staff have to do is sign a waiver whenever we work on a non-AEA show for the school. The waiver is pretty boilerplate: "part of our educational responsibilities as faculty/staff"...Our business rep has been dealing with the school for years, and she knows we don't exploit AEA members.
Even though the waiver is on a case-by-case basis, Equity has never denied approval...
As far as teaching goes, the University determines when I teach, but they're careful to allow me an hour and a half between my class and my call for rehearsals.