How do I display custom post types through a common taxonomy?

You can use pre_get_posts hook to add your custom post type to the query

function include_recipes( $query ) {
    if ( $query->is_category ) {
        $query->set( 'post_type', array('post','recipes') );
    }
    return $query;
}
add_filter( 'pre_get_posts', 'include_recipes' );