The main problem with Bohmian mechanics, from my perspective, is not that it is non-local per se (after all, the lesson of Bell's theorem is that all interpretations of QM will be non-local in some sense), but that it's particular brand of egregious non-locality makes it very difficult to come up with a relativistic version of the theory. I have seen some attempts at developing a Bohmian quantum field theory, but they have been pretty crude (relying on undetectable preferred foliations, for instance, which I consider anathema). I haven't been keeping track, though, so maybe the state of play has changed.