1st, look for the assign__terms user capability. If you don’t see it and it does not work if you try manually add it, then I can suppose that custom taxonomy is defined with default capability type. Try to add to a role ‘edit_posts’ and/or ‘manage_categories’ capability.
Hi I added these three capabilities (link to image attached)
assign_kb-cats_terms (though the category begins with underscore _kb-cats )
amd I also added assign_info_terms (by the name of the CPT they belong to)
I added the capabilities to the Author abilities
but in the add CPT ui I still see the checkboxes as disabled… (link to image attached)
Btw., I work on add custom taxonomies to the code executed for the URE’s option
“Force custom post types to use their own capabilities”. This will replace ‘edit_posts’ for such taxonomies with ‘assign__terms’ capability. So you will not need to add ‘edit_posts’ for custom post types. I plan to add this to the next udpate.