I think it is pretty much unanamous! Spears should also be allowed!
Shotguns are very capable deer-getters. There is no reason that rifles, handguns and bows should be outlawed though!
I know some states are shotgun only, because of population density. While I know that rifle bullets will go much farther, a good shotgun slug will travel pretty far too. So, I'm not sure that these states are right in limiting weapons to shotgun only!
Teaching people to be responsible might be just as good or better. Always knowing what you are shooting at, and what is beyond the target too, is the first thing any new hunter should learn!