I have custom taxonomies which up until 4.4 worked fine. Now when I go to /wp-admin/edit-tags.php?taxonomy=gmc_dietary&post_type=gmc_recipe I get the message:

You are not allowed to manage these items

If I change show_ui to true then I can get to the page again but I don’t want the features that changing that brings.

register_taxonomy('gmc_region', 'gmc_recipe', 
    array(
      'labels' => array( 
        'name' => __( 'Regions', 'gmc'), 
        'singular_name' => __( 'Region', 'gmc'),
        'popular_items' => NULL,
        'search_items' => __( 'Search Regions', 'gmc'), 
        'all_items' => __( 'All Regions', 'gmc'),
        'edit_item' => __( 'Edit Region', 'gmc'), 
        'update_item' => __( 'Update Region', 'gmc'), 
        'add_new_item' => __( 'Add New Region', 'gmc'), 
        'new_item_name' => __( 'New Region Name', 'gmc'),
        'menu_name' => __( 'Regions', 'gmc'),
      ),
      'rewrite' => array( 
        'slug' => 'regions',
        'with_front' => false
      ),
      'show_in_nav_menus' => false,
      'show_ui' => false,
      'show_tagcloud' => false
    )
  );

What am I doing wrong?

First off, the link you provided is the wrong taxonomy, the below is correct:

/wp-admin/edit-tags.php?taxonomy=gmc_region&post_type=gmc_recipe

The parameter causing the issue is show_ui => false which used to tell WordPress not to show the metabox for managing the category but now it turns the Taxonomny into a Private Taxonomy so it cannot be managed by the user ( using the User Inerface ).

If you want to remove the metabox or the admin menu you’ll have to do it manually:

Remove Metabox

/u/Toscho pointed out in chat if you want to not display the metabox you can pass false to the meta_box_cb parameter on register like so:

register_taxonomy('gmc_region', 'gmc_recipe', array(
    'labels'                => array( 'labels' => 'etc' ),
    'meta_box_cb'           => false,
    'show_in_nav_menus'     => false,
    'show_ui'               => true,
    'show_tagcloud'         => false
) );

OR you can remove them manually ( as you can with any metabox ) by doing the following:

function theme_hide_metaboxes() {
    remove_meta_box( 'gmc_region_typediv', 'gmc_recipe', 'side' );  // Remove Region Taxonomy Metabox
}
add_action( 'do_meta_boxes', 'theme_hide_metaboxes' );

Remove Admin Menu

function hide_admin_menu_items() {
    remove_submenu_page( 'edit.php?post_type=gmc_recipe', 'edit-tags.php?taxonomy=gmc_region&post_type=gmc_recipe' );
}
add_action( 'admin_menu', 'hide_admin_menu_items' );