Hidden variables theory was not disproved. Local hidden variables theory was disproved, but, actually, all local theories of any kind whatsoever that say that experiments have definite results have been disproved.
EPR is the argument that showed any local theory agreeing with the results of quantum experiments must have hidden variables. Bell showed that any hidden variable theory must be non-local. Conclusion: theory is non-local.
Many worlds escapes this by not having definite results of experiments or anything else. Since anything that could happen does happen, there is no need for non-local communication to achieve the (non)results.
Bohmian mechanics is a mathematically consistent theory (uniqueness and existence proven for a wide range of Bohmian systems) and it gives rise to an explanation of the quantum formalism. One can choose to dismiss because of prejudice, but there is no mathematical or physical reason to do so. Its biggest flaw, being nonlocal and thus philosophically (not actually) incompatible with relativity, is what Bell established as having to be the case for any theory with results.
The story with quantum field theory is more questionable, but there is a perfectly fine setup with creation and annihilation of particles, thereby being compatible in spirit with much of QFT. The biggest problem is that technically QFT has problems with having a well-defined wave function. But there have been Bohmian inspired methods of solving that problem, basically using boundary conditions that respect the preservation of probabilities under annihilation and creation.