Non-local realism involves the idea that there can be faster than light communication between objects in different parts of the universe. This goes against relativity and all current evidence from science. Here,
Principle of locality - Wikipedia
The special theory of relativity limits the speed at which all such influences can travel to the speed of light,c. Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point.
Einstein's principle of local realism is the combination of the principle of locality (limiting cause-and-effect to the speed of light) with the assumption that a particle must objectively have a pre-existing value (i.e. a real value) for any possible measurement, i.e. a value existing before that measurement is made. However, Fine's theorem shows that this deterministic assignment of properties is not required to prove Bell's theorem.[5] This is because the set of statistical distributions for measurements on two parties, once locality has been assumed, are independent of whether or not determinism is also assumed. This result demonstrates that one can consider local realism as the statement that real states exist independently of the observer (realism), combined with the assumption that two separated systems each have their own states with local dynamics (locality).
Here an easy way to understand the problem,
» Local realism is dead, long live local realism?
Believing that there is instantaneous communication and active conspiracy between particles to confound our experiments to preserve the ideology of realism seems to me to be a bit like young earth creationists beliefs that "earth was created in six days but made to look like its old".
I'd also point out that non-locality has dramatic effects on our notions of causality.
If there is faster than light interaction, there is some frame in which the interact goes *backward in time*. In other words, events in the future (in that frame) are causes of events in the past.
That automatically bring non-locality into question. Even to the extent that causality makes sense, it should be limited to the future light cone of the cause. Non-local causes violate that rule.
But, and more importantly, the simple fact that quantum mechanics correctly predicts the behavior of any number of actual, physical systems is enough to take it seriously. And QM is a local, non-realist theory. That is very good reason to both suspect that realism is false and that locality is true.