Nope, turns out it’s not the other plugin. At least, not entirely.
When used in conjunction with the plugin Gravity Forms – Update Post, this plugin does not allow taxonomies to be updated because GFCPTAddonBase->save_taxonomy_field() passes wp_set_object_terms() a value of “true” for the “append” argument.
Since this plugin is purely aimed at creating new posts for which it’s reasonable to assume no terms exist that argument can (and should) be false. If nothing else, for the sake of being a good neighbour and not breaking the other plugin.