This is a tough one, isn’t it? Some people come away from this passage believing in absolute pacifism. I haven’t been able to do that, but it is a question worth struggling over.
For sure, though, we are taught here not to retaliate in the normal human ways. We don’t strike back when we are insulted. We don’t defend our property. We don’t hold on to our stuff.
In short, we aren’t all that concerned with our “rights”. We are more concerned with the people around us than we are with ourselves.
I don’t think Christians are to give everything away and live in poverty. Not most of us, anyway. But I do think we have to show ourselves to be different in the way we treat people.