Ah, you are correct.
I suspect that a pilot-wave physicists’ answer to that may just be that non-globally-hyperbolic spacetimes are unphysical solutions of GR. (As far as I know, our observations of the universe are consistent with a globally hyperbolic spacetime - is that correct?) If the conceptual problems of bringing GR and quantum physics can be resolved by pilot-wave theory, then it is worth exploring in that direction, even if it means ruling out some intriguing possibilities from classical GR.
The question of whether non-globally-hyperbolic spacetimes are possible also gets into the philosophy of time - A-theory vs. B-theory and so on - and the question of what Bell’s theorem means for the compatibility of QM and relativity. But that is perhaps a question for a different thread.
So, these phenomena are related to the way that the pilot-wave theory explains/derives the Born probability rule. (Here’s a recent article on that topic, which provides a synthesis of two previously somewhat-competing explanations.) The upshot of the explanation is that in a typical universe governed by Bohmian mechanics, it is extremely probable that any ensemble of systems prepared in a corresponding way (e.g. a collection of electrons describable by the same wavefunction, sent one-at-a-time through a pair of slits) will obey Born rule statistics. (And this explanation would carry over to any other pilot-wave theories that preserve certain core features of Bohmian mechanics.)
But, according the the theory, there is the remote possibility that we could find some ensemble of systems that happens not to obey Born rule statistics. We never have, so none of these phenomena have been tested and this is all hypothetical. But if we did find such an ensemble, and if it had certain properties, a number of new phenomena would be available to us: including undetectable eavesdropping on quantum cryptography key distribution, extremely powerful quantum computation, and faster-than-light signalling (with a preferred foliation, so no time-travel paradoxes).
We’ll probably never get to access these new phenomena, but if we did, it would be pretty decisive evidence in favour of pilot-wave theory (not to mention, providing a fantastic example of fine-tuning in physics).