I have been to N.O. a couple of times, but perhaps I was not observant.
The gesture from Montana drivers was not really a wave, but they just lifted fingers from the steering wheel and waved them.
Come to think of it, at my 2nd home in the AZ high country boondock, we do the same when running across a driver in the other direction, as a way of acknowledging them. However, it is only done when you are on a local road and the other driver may be living nearby, an unknown neighbor. We do not do that on major thoroughfare. When the other driver yields to you, of course it is different, and we use hand gestures as an acknowledgement to thank.
In Phoenix, if you wave to strangers for no reason, people will think you are crazy. Montana has only 1 million residents for a fairly large state, and most people live in small towns. Even the largest city of Billings has but 100,000, and its downtown is not what many think of a downtown. I stayed at a town of 4,000 with a 1-block downtown. So, the mentality is definitely different than even in Arizona.