Why does local realism being wrong imply that non-local reality is true? Such is widely opined to be the only sober solution because it conserves good old reality, the scientists’ fort that is to be defended against the onslaught of magic.
However, reality with “spooky actions at a distance” is not non-magical either. Nevertheless, the issue is known as “non-locality in quantum physics”, never as “non-reality in quantum physics”. How about keeping localism and instead accepting that realism is a god of the gaps in retreat? Don’t like it? Well, how about at least not being so sure about it for starters?
If you desperately cling to reality fighting against pseudo-sciency magic, you may well end up with nothing less but “magic realism”. That’s not what you wanted.
Modern science has disproved naïve realism: There is no locally realistic description of our world possible. We can approach this insight from different directions, for example by explaining that 'real stuff' cannot provide an acceptable fundament ‘at the bottom’. However, anybody with some interest into science and philosophy should work through one of the rigorous proofs of ‘non-locality in quantum physics’ at least once. This issue is the most important piece of philosophically relevant physics mankind has discovered; there is no excuse to be ignorant about it.
The proof is one ad absurdum: One tentatively assumes that everything depends only on what is locally present in form of ‘real stuff’; that Bob’s random decisions done far away do not influence Alice’s random choice for example. A certain relation, namely Bell’s inequality, is then obviously valid, but the experimental observations clearly violate that relation.
A lay-person-accessible yet still watertight version of the established proof introduces what is actually observed in experiments with photons and then shows by contemplating tennis balls that it is impossible to account for what is observed inside a locally realistic framework.
Local realism cannot possibly describe the world as it reveals itself to us in the laboratory. One of them has to go, the here or the real. Einstein was a realist and believed that the only resolution of this issue could be that somehow Bob’s random choice immediately changes the hidden variables at Alice’s place or vice versa. This would imply faster than light interaction and so Einstein got his pants all in a knot about it. In 1947, Einstein wrote to Max Born that he could not believe that quantum physics is complete "because it cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance."
Some find it obvious that we need to abandon localism but not realism, because somehow, realism is obviously the more sober, proper, scientific position that guards against crazy, obscure idealism. This clinging to realism blinds itself against the fact that a non-local reality is so spooky (read “spooky action at a distance”) that it is actually much less sober than keeping localism instead. Localism is a very successful piece of physics, while realism is the god of the gaps in awkward retreat.
The advanced way to think about these issues is the way Hugh Everett for example did it. The description is in terms of local physics, however, what is “real” becomes relative. Many refuse Everett relativity because they confuse it with multiple worlds interpretations (MWI) and multiverses. These are not the same. In fact, MWI are at times monstrosities of desperate realism while Everett relativity is a necessary improvement in terminology consistent with antirealism.