Movies where the thematic elements revolve around a group of people banding together against an oppressive force, but not really a chosen one style story. I have Braveheart in mind but I don't know if that really hits the same notes, because so much of it is also a love revenge story.
Star Wars. I think it came out in 1977.
Luke Skywalker's story is definitely a chosen one style story. He's the son of the big bad guy!
luke... literally isn't the chosen one
Kinda? His arc is mostly self contained. He doesn't have any particular role in actually destroying the second death star. That's one of the things i like about the ot - the space wizard plot and the military plot move in tandem but aren't really dependent on one another.