Abner Shimony spent his whole career writing papers on quantum spookiness, and here is his opinion of the consequence of Bell's Theorem:
There may indeed be "peaceful coexistence" between Quantum nonlocality and Relativistic locality, but it may have less to do with signaling than with the ontology of the quantum state. Heisenberg's view of the mode of reality of the quantum state was briefly mentioned in Section 2 - that it is potentiality as contrasted with actuality. This distinction is successful in making a number of features of quantum mechanics intuitively plausible - indefiniteness of properties, complementarity, indeterminacy of measurement outcomes, and objective probability. But now something can be added, at least as a conjecture: that the domain governed by Relativistic locality is the domain of actuality, while potentialities have careers in space-time (if that word is appropriate) which modify and even violate the restrictions that space-time structure imposes upon actual events. The peculiar kind of causality exhibited when measurements at stations with space-like separation are correlated is a symptom of the slipperiness of the space-time behavior of potentialities. This is the point of view tentatively espoused by the present writer, but admittedly without full understanding. What is crucially missing is a rational account of the relation between potentialities and actualities - just how the wave function probabilistically controls the occurrence of outcomes. In other words, a real understanding of the position tentatively espoused depends upon a solution to another great problem in the foundations of quantum mechanics - the problem of reduction of the wave packet.What he is trying to say is that Heisenberg's quantum states represent potential measurements, not actual reality. There are apparent nonlocalities in the potentialities, but that is just in our minds. It does not violate relativistic causality, because that is about actual reality. There is no nonlocality in actual reality.
He still wants to believe in some sort of spookiness, but this shows that there is no proof of nonlocality in actual reality.