According to a growing chorus of voices (see, e.g., a number of papers in this volume), (i) there are strong grounds for accepting a realist construal of quantum mechanics (QM), and (ii) the most plausible interpretations of QM entail that the wave function is a real entity that exists in a configuration space of very, very many dimensions (about 3x10 to the 80th, according to current estimates). But it's not at all clear how the ordinary three dimensions of our experience can be accounted for via this configuration space. In fact, some (e.g., Alyssa Ney) have argued that they probably can't, in which case there is non-trivial epistemic pressure to think the three dimensions of ordinary experience are, in an important sense, mirage-like (L.A. Paul has similar worries, but doesn't explicitly come down on the matter one way or the other. Jill North and Jenann Ismael have stronger suspicions). But if so, then there is non-trivial epistemic pressure to think that ordinary perceptual experience is massively unreliable.
Now according to many theists, if God exists, then God designed us in such a way as to ensure that our perceptual faculties reliably track the truth about the world, where this includes beliefs about the ordinary objects of experience having extension in length, width, and depth. But if the above worry is at all on track, then ordinary perceptual experience is massively unreliable. And if that's right, then something has to give: either (i) theism is false, or (ii) the existence of the God of theism doesn't make it likely that our perceptual faculties are reliable. The first disjunct is of course fatal to theism. The second might well be equally so, given a few more premises concerning God's omni-attributes and a bridge principle from those attributes to the reliability of sense perception. However, even if this can't be done, the second disjunct still causes trouble for a number of theistic apologetic strategies. For example, it would be devastating to Plantinga's theory of warranted Christian belief. Either way, then, if the growing chorus is onto something, troubling epistemic consequences for theism follow.