I think a compelling government intrest in the case of explosives could be and has been made. The indiscriminate nature of explosives, and hazards associated with their storage and use, are such that reasonable regulation could meet a strict Constitutional test.
Light support weapons, like full-auto LMGs, could be argued either way.
Actually I'm mostly okay with how things are right now in many states: you can buy most any common weapons without any restrictions; you have to have a Class III license for full-auto or grenade launchers, with storage requirements. The main thing I'd change is removing selective-fire "assault rifles" from the Class III list and returning them to unrestricted status.