Post formats disabled, still the plugin's menu option appears

Hi, interesting question ??

The point is that the plugin shows all taxonomies that are set to public. The builtin ones are set to public in WP-core.

You can however overwrite that, by just registering them again, this time with public set to false. It needs to happen in the init action, but with a late priority. Use it like this (works for me). It has been cut-and-pasted from wp-includes/taxonomy.php, with only public set to false.

add_action( 'init', 'i_like_disco', 12 );
function i_like_disco() {

	global $wp_rewrite;

	$rewrite = array( 'category' => false, 'post_tag' => false, 'post_format' => false );

		/**
		 * Filter the post formats rewrite base.
		 *
		 * @since 3.1.0
		 *
		 * @param string $context Context of the rewrite base. Default 'type'.
		 */
		$post_format_base = apply_filters( 'post_format_rewrite_base', 'type' );
		$rewrite = array(
			'category' => array(
				'hierarchical' => true,
				'slug' => get_option('category_base') ? get_option('category_base') : 'category',
				'with_front' => ! get_option('category_base') || $wp_rewrite->using_index_permalinks(),
				'ep_mask' => EP_CATEGORIES,
			),
			'post_tag' => array(
				'hierarchical' => false,
				'slug' => get_option('tag_base') ? get_option('tag_base') : 'tag',
				'with_front' => ! get_option('tag_base') || $wp_rewrite->using_index_permalinks(),
				'ep_mask' => EP_TAGS,
			),
			'post_format' => $post_format_base ? array( 'slug' => $post_format_base ) : false,
		);

	register_taxonomy( 'category', 'post', array(
		'hierarchical' => true,
		'query_var' => 'category_name',
		'rewrite' => $rewrite['category'],
		'public' => false,
		'show_ui' => true,
		'show_admin_column' => true,
		'_builtin' => true,
	) );

	register_taxonomy( 'post_tag', 'post', array(
	 	'hierarchical' => false,
		'query_var' => 'tag',
		'rewrite' => $rewrite['post_tag'],
		'public' => false,
		'show_ui' => true,
		'show_admin_column' => true,
		'_builtin' => true,
	) );

	register_taxonomy( 'post_format', 'post', array(
		'public' => false,
		'hierarchical' => false,
		'labels' => array(
			'name' => _x( 'Format', 'post format' ),
			'singular_name' => _x( 'Format', 'post format' ),
		),
		'query_var' => true,
		'rewrite' => $rewrite['post_format'],
		'show_ui' => false,
		'_builtin' => true,
		'show_in_nav_menus' => current_theme_supports( 'post-formats' ),
	) );

}

Thanks a lot for your reply Marcel!

I’m not comfortable with copying a core function in my theme, though.

It should be safe. It is not a function you overwrite, but the builtin taxonomies.
But you do have to be aware that when setting public to false, that the archives pages are disabled then.