Perhaps just call this update_tags instead of update_tags_object. If it is so generic that it can update "objects", there's no need to be explicit about what kind of tags it can update in the name anymore. It made sense for _issue, since you needed to distinguish what kind of tags it could and could not update.

Consider using isinstance here instead of passing in objtype explicitly.

Same here. I would just call this add_tag now instead of add_tag_object.

Looks good in general. I left a couple cosmetic, non-blocking comments above. :+1:

Same here. I would just call this add_tag now instead of add_tag_object.

I have renamed update_tags_obj to update_tags but kept the
add_tag_object and remove_tags_object as there already is a
remove_tags that has a different goal.

:+1:

Thanks for the review!