After looking more closely at the (default) Categories and Tags, and comparing them with the (custom) Genres and Authors I realised that although it looked like they were mixed, there were actually duplicates. e.g. the Tag ‘A S Byatt’ had a different ID to the Author ‘A S Byatt’. And the Tag ‘A S Byatt’ had no Posts associated with it.
So, I held my breath and, in the WP Admin, deleted all of the Categories and Tags that had no Posts associated with them. All the Genres and Authors remained and everything now works as it should.
I guess at some point during my development, something went wrong and all the Genres and Authors were copied into the Categories and Tags taxonomies. I’ve no idea how that happened…