Exclude categories For Custom post types

You’d probably be better served by creating a custom taxonomy to accompany your custom post type. That way you can manage terms separate from the built-in categories taxonomy.

// Register Custom Taxonomy
function wpse_168762_create_gallery_taxonomy() {

    $labels = array(
        'name'                       => _x( 'Gallery Categories', 'Taxonomy General Name', 'text_domain' ),
        'singular_name'              => _x( 'Gallery Category', 'Taxonomy Singular Name', 'text_domain' ),
        'menu_name'                  => __( 'Gallery Categories', 'text_domain' ),
        'all_items'                  => __( 'All Gallery Categories', 'text_domain' ),
        'parent_item'                => __( 'Parent Gallery Category', 'text_domain' ),
        'parent_item_colon'          => __( 'Parent Gallery Category:', 'text_domain' ),
        'new_item_name'              => __( 'New Gallery Category Name', 'text_domain' ),
        'add_new_item'               => __( 'Add New Gallery Category', 'text_domain' ),
        'edit_item'                  => __( 'Edit Gallery Category', 'text_domain' ),
        'update_item'                => __( 'Update Gallery Category', 'text_domain' ),
        'separate_items_with_commas' => __( 'Separate Gallery Categories with commas', 'text_domain' ),
        'search_items'               => __( 'Search Gallery Categories', 'text_domain' ),
        'add_or_remove_items'        => __( 'Add or remove Gallery Categories', 'text_domain' ),
        'choose_from_most_used'      => __( 'Choose from the most used Gallery Categories', 'text_domain' ),
        'not_found'                  => __( 'Not Found', 'text_domain' ),
    );
    $args = array(
        'labels'                     => $labels,
        'hierarchical'               => true,
        'public'                     => true,
        'show_ui'                    => true,
        'show_admin_column'          => true,
        'show_in_nav_menus'          => true,
        'show_tagcloud'              => true,
    );
    register_taxonomy( 'gallery_category', array( 'gallery' ), $args );

}

// Hook into the 'init' action
add_action( 'init', 'wpse_168762_create_gallery_taxonomy', 0 );

To attach the custom taxonomy on the other end (register_post_type), you would amend your ‘taxonomies’ parameter to 'taxonomies' => array('gallery_category'). If you needed to attach multiple taxonomies, it would be 'taxonomies' => array('gallery_category','category')

It’s still required to register the custom taxonomy for this to work.

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