A pure fusion bomb would produce less (not zero) fallout. Neutron activation would still produce some fallout, but you wouldn't have the fission byproducts like caesium-137, iodine-129 or strontium-90.
This is probably a bad thing; politicians might decide the bombs are clean enough to use.
even without actual radioactivity, pure fusion bombs would still be politically radioactive. look at the fallout (so to speak!) from the Hafnium controversy. they nixed all the research and stopped looking, after realizing that nuclear isomers would do little for energy storage (due to emitting energy as gamma radiation) but lots for bypassing restrictions on fissile materials.
To be clear, pure fusion bombs would still emit massive amounts of radiation. Gamma rays, x-rays, thermal radiation, all off that EM radiation would be emitted just like a regular fission bomb. Neutron radiation too. You'd have less (not zero) contamination of the earth itself afterwards, but everybody in the area would still be very badly irradiated.
I don't know enough about the Hafnium controversy to comment on it.
This is probably a bad thing; politicians might decide the bombs are clean enough to use.