What you describe is causality depicted as Laplace's daemon. I don't subscribe to such view, and neither does the modern science. The atheists you argue with on Twitter are mostly, as far as I could see, rather uneducated and just parrot some catchy sciency sounding phrases they themselves don't understand. Not that dissimilar to religious and spiritual believers.
But there are several things to consider. First, causality is basically the flow of entropy. That's basically what second law of thermodynamics describes. Now, while you can locally reverse entropy – a good example is life – and sending qubits “back in time” was, indeed, demonstrated, there is no known example of immortal living entity and the experiment with qubits has some catches, too.
While the authors speculate that they violated second law of thermodynamics, when you consider the energy of the whole involved apparatus, that claim is simply false – when the whole Universe is considered (which it must be), the entropy was reversed only locally at the expense of increase of entropy elsewhere in the system (i.e. Universe).
Furthermore, “[t]he researchers found that in 85 percent of the cases, the two-qubit quantum computer returned back into the initial state. When three qubits were involved, more errors happened, resulting in a roughly 50 percent success rate.” That is, the more complex the structure, the less likely it can violate second law of thermodynamics even locally. Well, life is sort of a miracle in this regard.
Second thing to consider is, then, that (and contrary to Einstein's sentiments) while God does, indeed, play dice, he does not throw one d6 at a time (which would result in completely random 1/6 linear distribution, i.e. all six numbers would be equally probable). When you throw only three d6, you already get a rough approximation of Gaussian distribution. Now, imagine all the “cosmic dice” that are continuously cast. So, while theoretically there might be a possibility to pass through a wall, the probability of it is either insignificantly minuscule or the feat is outright impossible (you e.g. cannot throw a “1” or “2” with three d6).
Just as a side note, evolution does not depend on 100% random gene mutations only. It also depends on screening against environment, i.e. fitness, which is causal. And of course, genetic changes are not 100% random -- there is also epigenetics, which, again, is causal.
Last thing I'd like to address is that most “extraordinary” experiences are “read operations.” And as it seems, technically, you can derive all information (past and present) from every point in Universe. Now, our senses typically gather much more data than we are aware of, and brain (let's set aside its physicality for a moment) is known to be susceptible to stimulation completely outside the range of our senses.
All of that could explain remote viewing, telepathy, oracles (with or without attention focusing tools such as cards, sticks, coins, arrangement of celestial bodies, and similar, but also the more brutal methods used in the past), disembodied entities (ghosts, spirits, fairies, angels, but also aliens, and so on), etc. The data itself is valid, only its representation reflects our lore and private symbolic vocabulary. (Hence, also the confusion that plagues this "field". Also, if everything was linearly random and there was no causality, oracles would not work.)
As for magic (or sorcery) as an act of influencing, maybe it could be simply a case of influencing the “read operations” of others combined with ensuing placebo effect (which is basically a self-induced body reaction, not that it's a pure mind construct as many people think).
All in all, I like to picture Universe as a big causal river of entropy with various intermingling streams of itself. Of course, we as the whirlpools have free will and cast our own dice, but we are always limited, if by nothing else, then at least by the fact that we, as humans, are (of) the river. And frankly, from the perspective of “true nature”, Universe won't be here forever – that river started and it will also end one day.
