A more socially acceptable nuclear weapon: Neutron bombs
globalsecurity.org
globalsecurity.org
Neutron bombs are full fledged thermonuclear bombs where the uranium casing around the secondary is replaced by a beryllium casing. The uranium liner would normally absorb the fusion neutrons produced by the secondary and fission to increase explosive yield, instead the fusion neutrons multiply in the beryllium increasing neutron yield.
The neutron bomb still has a fission primary, and even the smallest will still produce nuclear explosions equivalent to multiple tons of TNT and release radioactive fallout into the environment. In fact, the bulk of nuclear fallout is actually not from the bomb itself, but from material in the environment irradiated by a nuclear explosion's neutrons. The idea of a bomb that kills people but leaves structures unmarred is a myth.
The reason neutron bombs were developed was to be used for defeating tanks and similar armored vehicles. Tank armor is very resistant to the pressure wave damage that nuclear weapons produce. Tests indicate tanks can survive detonations of small nuclear detonations within a few dozen meters. Given that in combat tank formations would be spread out over many kilometers, the odds of taking out more than a small handful of targets with a single nuke is actually quite small.
Neutron bombs can produce neutrons that will penetrate armor that its pressure wave can't. This means a relatively small number of nuclear weapons can defeat a large number of tanks. However because of their use case, neutron bombs would invariably be detonated close to the ground where they would produce lots of fallout and their actual effectiveness is questionable. While neutrons can penetrate some armors quite well, there are specific armor compositions that are quite resistant to neutrons. Boron is an excellent neutron absorber, so it would be relatively easy for an army expecting a nuclear engagement to put boron carbide panels on their vehicles. Depleted uranium, ironically, is actually one of the best neutron shielding materials by weight, which likely contributed to the decision to use depleted uranium in non-export Abrams tank armor (note that it also has many other desirable properties for the task). Combined with the fact a large scale tank battle between peer nuclear states is unlikely anytime soon and it's easy to see why there was little incentive to continue work on neutron bombs.
Certainly no one should view neutron bombs as more acceptable nuclear weapons. Acute radiation poisoning is a terrible way for a soldier to go, and ground burst fallout is difficult to limit, meaning large numbers of civilians could be irradiated as well. Such weapons would need to be deployed in large numbers and spread out among many stations along a front which is inherently insecure, dramatically increasing risks of accidents, inappropriate use, and proliferation. If you are not comfortable with the large scale deployment of tactical nukes, you should not be comfortable with the large scale deployment of tactical nukes with lethality cranked to max.