If I'm understanding you, what you're describing sounds more to me like a threat or warning signal than an attack itself... potentially very dangerous because of what it predicts and because of the psychology it's telling you about, more than it is dangerous in and of itself in a directly physical way. I.e., dangerous because they're on the verge of attacking you in a more serious way, rather than because they already have?
In any case, how do you respond to it? Do you respond in a physical way with some 'technique' (beyond stepping out of the way)? If as you say it's a way of saying 'give me a reason to kick your ass', or issuing a challenge, then does that mean there's still a chance of just walking away?
I think it is a remarkably difficult question which is why I find it so bothersome that some kind of wave it away giving a simple answer. That shove could be posturing. But it could also be someone near the breaking point.
The problem with these discussions is that context matters a great deal. And what you do will depend greatly on that context. The danger here, in my mind at least, is the dismissal of these things as being "just" one thing or another. Life is rarely that simple.
I've been shoved. I've been in fights. I've been attacked. Sometimes it is just posturing -- once was a guy at a restaurant who was yelling at his wife/girlfriend/date/whatever. He was getting *very* agitated and I went up with another friend trying to calm him down. He gave me a not-so-friendly shove. However, I grounded myself and barely moved. That was enough with this guy to start backing down (not to mention the guy I was with was even bigger than me). I wasn't threatening, I was trying my best to calm him. When he shoved my reaction was to ground it but I was ready to take him down depending on how he behaved. Once he realized I wasn't going to be easy to push around and that I wasn't at all impressed with him he seemed to lose his desire to get more angry. But he still stomped off in a huff.
Another time a guy pushed at a bar totally unprovoked (best I could tell). I was just walking through the crowd and he decided I was too close/had the wrong look/whatever. He pushed hard and I didn't see it coming. I was pushed into some other guys and the guy came at me very quickly only to get slammed by the bouncer who saw the whole thing.
Those are my experiences. I don't have easy answers. And *that* I think is the "correct answer" -- namely that it ain't quite so simple. I just caution people against thinking that a push is "just" one thing or another. Sometimes a shove is a blind rage attack. Sometimes it leads to something else. Just be careful of assuming you're going to be able to just put your hands up and say "whoaaa, cool down". What you might get is a punch to the face for your trouble.