Without some notion of space-time you could not have a meaningful notion of locality, therefore Bell's Theorem is a non-issue. But you don't need a relativistic

Without some notion of space-time you could not have a meaningful notion of locality, therefore Bell's Theorem is a non-issue. But you don't need a relativistic space-time for Bell's Theorem, any space-time in which physical influences travel at a bounded speed will suffice. Bell's Theorem does, however, create an uneasy tension between quantum theory and special relativity. Tim Maudlin writes quite a good book about this called "Quantum Non-Locality and Relativity".