A pure fusion device would create many radioactive byproducts when neutrons and gamma rays interact with the atmosphere, bomb casing, and any other matter in the way.
Gamma rays don't make things radioactive. The neutrons might be another matter, but the fact remains that the vast majority of lingering radiation ('lingering' meaning anything lasting longer than the prompt radiation emitted during the explosion) produced by a thermonuclear blast comes from the fission components of the bomb.
E.g. the Tsar Bomba was not only the biggest nuclear blast ever, but also very 'clean', due to nearly all of its yield coming from fusion.
"The explosion is one of the cleanest in the history of atmospheric nuclear tests per unit of power. The first stage of the bomb was a uranium charge with a capacity of 1.5 Mt,
[37] which in itself provided a large amount of radioactive fallout; nevertheless, it can be assumed that Tsar Bomba was relatively clean – more than 97% of the explosion power was provided by a thermonuclear fusion reaction, which does not create a significant amount of radioactive contamination."