Education

You can't moonlight for pay in the same field. You would be competing with the union.

I don't know of any specific teachers union bans on the practice, but I do know that in some areas, you can hire a (certified teacher) tutor directly from the union (or sometimes from a for-profit subsidiary of the union). It wouldn't be a big stretch to imagine that those unions wouldn't allow their members to moonlight in competition with them (sometimes through the county schools).

It's also possible that the movie is (gasp!) lying. I haven't seen it, but I'd bet that if a union told its members not to provide unpaid after-school tutoring (which so many teachers do as a matter of course), that the producers of the film might spin that as a "ban on teachers tutoring after school".