The fallout from a bomb is going to depend on its design.

In a typical thermonuclear bomb, most of the yield is still from fission, so there are lots of fission products. The purpose of the fusion is to generate neutrons to more thoroughly fission the fissionable material.

However, it's possible to design thermonuclear bombs with greatly reduced fission fraction. The extreme example of that were the Ripple tests, which the US conducted shortly before atmospheric tests were banned. These involve a secondary without a fission "spark plug", where carefully tailored implosion cause the density/temperature at the core of the secondary to reach conditions for fusion ignition, in a way very similar to how inertial confinement fusion reactors are imagined to work. The most extreme of these has been reported to derive 99% of its yield from fusion reactions. If the neutrons from these are absorbed in something with low activation the fallout could be greatly reduced.