Other interpretations of quantum mechanics do not generally violate Bell's Theorem, since it appears to be confirmed by experiment. There are other interpretations which choose to abandon locality rather than hidden variables, such as the De Broglie-Bohm pilot wave interpretation. But consistent histories doesn't even do that. It's actually pretty similar to the Copenhagen interpretation.
I didn't say anything about violating Bell's theorem. Yes pilot wave theory is a better alternative that doesn't require spooky action at a distance but consistent histories doesn't require wavefunction collapse (which is a huge source of spookiness as well).