There is no basis on which to posit a law of causality, accoording to the argument that we never observe causes . When two billiard balls collide all we observe motion, and apparent contact (?), but what does the cause look like? Can you describe 'the cause'?
More specifically, let us say that there is a moment in time T when the two balls are in contact. We imagine them (as Newton would) as mathematical circles tangent at exactly one point. At any time t > T we have the circles moving apart. The question is: at time T, what happens that we call the cause?
Some descriptions of classical physics say that something is transfered, but we do not observe the thing which is transfered; this supposed transfer is analogous to epicycles, or some other such positivist mechanism. Its no concern because we have alternatives to sloppy language.
Now, as for this nonsense about QM and causality, please do not repeat what you read in popular level books, and what you have seen qualitatively described in lectures. If it upsets you that those books contain false information, lies for you to 'learn', then please do your part to stop repeating the information, so that lies from the newspapers of the first half of the century can finally die.
Lets examine:
Actually, that's the symmetry of the laws of nature that you're referring to - not just conservation of momentum. It's the fact that (as far as we know) if you do an experiment in a different place, or a different time, or at a different angle, then as long as the experiment is the same, you will get the same result (except for quantum uncertainty, but we need not get into that).
What you are saying is exactly right, on a differentiable manifold with certain properties. Don't confuse nature with a differentiable manifold! All of theoretical physics, including QM, assumes the law of causality (and much more that is no philosophically taken for granted), so Physics does not apply to this thread.
In fact, the problem with causality is that it is a necessary part of the human experience, but we mistakenly extrapolate it to something real in the world, which it is not (just like emotions are not real in the world).