You have heard it was said, "An eye for an eye, and a tooth for a tooth." But I say to you, do not set yourself against the man who would wrong you. If anyone strikes you on the right cheek, turn to him the left cheek also; and if anyone would sue you and take your coat, let him have your cloak as well; and if anyone forces you to go one mile, go with him two miles.
I used the New English Bible's translation of that second sentence, because it doesn't involve the notion of resisting, or not resisting, 'an evil man'. Probably it's a bad idea to assume that someone giving you grief is 'evil'. Also, this doesn't end up saying you shouldn't try to prevent evil happening to self and others, but that you shouldn't 'set yourself against' the perpetrator, shouldn't think of yourself as 'fighting' him per se. Should not [as I've always taken this] damage anyone else in the process of trying not to get hit...
By now it's a familiar interpretation to most everyone studying this stuff, that the following parts imply a kind of psychological judo in response to anyone treating you shamefully: 'If he's giving you an off-hand slap, make him have to consider respectfully slugging you. If he's taking your clothes, strip yourself naked and embarrass him. If he's bullying you into forced service, do more than he has a right to ask [and his centurian will want to know why he's abusing the local population.] Jesus was calling for a form of nonviolent resistance, in other words.
Maybe, maybe not... The cultural implications of the details probably did mean that. But when, as a kid, I tried applying this to my parents, I just got even more indignant.
So far as all of this is about placing yourself safely under God's jurisdiction, it comes out on a different level: letting God take care of that stuff. There is no one worth your anger but God, no one else able to do you harm or good. Any trouble that comes your way must be serving God's purposes; anything you can do to mitigate it is also serving God's purposes -- but getting mad at the agent of that trouble is futile, is just multiplying the total suffering.
Getting mad at God... will not make God angry. When I do, though, eventually it occurs to me that God is more aware of what's happening, why, and how all this will work out.