Is it possible to translate this to layman terms?
Causality is local even in quantum physics. The "Spooky action at a distance" is just correlation
This leaves the "acausal action at a distance" aka nonlocal correlation. There is no controversy here. There is no superluminal messaging and there are no need for hidden variables and things like that. Entangled quantum _state_ of two distant entangled electrons has no coordinates in space. Quantum states are treated as ghosts.
For the authors there exist discord between instant correlation and special relativity. I have no idea what comes next. Somebody else should explain how Trace Dynamics works.
This assertion is ridiculous. The only fields "harder" (in the scientific sense) than modern physics are pure math fields. High-level physics is almost pure math anyway; much of it is abstract algebra and topology. That's not to say it's divorced from reality; reality seems to like using these principles under the hood.
The "soft" stuff you are talking about isn't modern physics; it's people taking (mostly uninformed) potshot guesses at how to interpret the hard results that modern physics offers. Within the physics community, these discussions are much more muted, because it's clear that the answers to physics questions won't come out of philosophical pontificating.
Physicists figure out which interpretations are compatible with experimentally verified theory, and then look for additional consequences of these interpretations that can be tested. Right now there are a number of plausible explanations of the observations of quantum mechanics, each with their own (often psychologically uncomfortable) way of dealing with its conclusions. It's rare to come across a physicist that is strongly convinced of one interpretation.
(This example, I hope, illustrates the difference between spooky correlation and causation. However, it is misleading about what really goes on in quantum mechanics. In quantum mechanics, the identity of our cards is not fixed after the deal, but remains in limbo until it is actually measured. And this limbo-like superposition state can be measured in different non-independent ways and these probabilities interact with each other and other probabilities. Nonetheless, even with all that added machinery, the general principle of correlation vs causation is the same as the two card example.)