Dystopian and PG? That's going to be tough. Dystopian films generally have a lot of "shoot people" in them on account of everything having collapsed. Admittedly some of them can get more gruesome than others. Also, if you go old enough (like pre-1985) a movie would get an R rating for "brandishing a shotgun." So...
Lets see here...
I, Robot (PG-13)
Aachi & Ssipak (Unrated..and animated..never heard of it)
Ghost in the Shell (two of the movies are PG-13, the first one is R, the TV series is probably closer to PG-13)
Metropolis (PG-13)
Sleep Dealer (PG-13)
WALL-E (G)
Titan A.E. (PG; fantastic, 10/10 have watched again)
I Am Legend (PG-13)
Waterworld (PG-13)
Batman Begins (PG-13)
Neon Genesis Evangelion - Movie: The End of Evangelion (Unrated, probably not a good choice, as no one knows what the ending means...the movie is an alternate ending and no less confusing)
Z.P.G. (PG)
1984 (from 1956, unrated)
Alphaville (unrated)
Silent Running (G)
Soylent Green (PG)
The Lego Movie (PG)
I'm going to drop Eternal Sunshine Of The Spotless Mind in, even though it's rated R and not technically a dystopian film, but it does touch on some things that are very dystopian. According to Rotten Tomatoes it's for language and "some drug and sexual content." I frankly don't recall any of it. I highly recommend it, even if you can't use it in the classroom.
I'd recommend Titan A.E., it was a kids movie from the 90s, I actually went and sought it out as an adult to watch it again. Z.P.G. is not one I've seen, but I think that would be a really good example (ZPG stands for Zero Population Growth and the kinds of society that makes that happen are generally pretty extreme). 1984 is, of course, a classic. And Orwellian. I'm surprised that the 1956 version was never rated. WALL-E and The Lego Movie your students have probably already seen, but serve as some foundational material they might not have picked up on. The theme song from Lego is
THE dystopian themesong. There is no other, as far as I'm concerned.
QUOTE
Rocks, clocks and socks they're awesome
Figs and jigs and twigs that's awesome
Everything you see or think or say is awesome
Everything is awesome
Replace every noun in the song that's stated as being awesome with things like "big brother" "espionage" "the NSA" and leave the tune intact. Remember
everything is awesome.