It is worth noting that in the original scripts, Johnny Rambo was a truly repellent and bloodthirsty monster who mowed down more than 150 people. Most of whom had nothing to do with messing with him. But by the time Stallone kept fiddling with the script because he wanted to play Rambo as an "underdog hero" in the "Rocky" mode, Rambo directly killed at most one or two law enforcement people. Both of whom were attacking him.
I believe in the original First Blood novel, Rambo kills the young hunter (and his father) who stumble onto him in the woods. In the movie, Rambo gets the kid down and threatens him with a knife but doesn't kill him. If you want Rambo to be a character the audience empathizes with, he can't be a cold-blooded killer. If he is, then the guy who's trying to stop Rambo is the protagonist. In that story, the heroic small town sheriff is trying to stop the deranged ex-Special Forces guy...
From what I've read, the Sheriff is the hero in the book and Rambo is the monster. Kind of like Moby Dick.