Example of a working WP_User_Query search by simple user meta using Simple User Listing In this example I am searching for users by the meta field "billing_city"

functions.php

<?php
/**
 * Place this in your theme's functions.php file
 * Or a site-specific plugin
 *
 */
 
// Switch the WP_User_Query args to a meta search
function kia_meta_search( $args ){

  // this $_GET is the name field of the custom input in search-author.php
	$search = ( isset($_GET['billing_city']) ) ? sanitize_text_field($_GET['billing_city']) : false ;

	if ( $search ){
		// if your shortcode has a 'role' parameter defined it will be maintained
		// unless you choose to unset the role parameter by uncommenting the following
		//	unset( $args['role'] );
		$args['meta_key'] = 'billing_city';
		$args['meta_value'] = $search;
		$args['meta_compare'] = '=';
	}

	return $args;
}
add_filter('sul_user_query_args', 'kia_meta_search');

// Register query var and whitelist with Simple User Listing
function kia_search_vars( $vars ){
	$vars[] = 'billing_city';
	return $vars;
}
add_filter('sul_user_allowed_search_vars', 'kia_search_vars');

search-author.php

<?php
/**
 * The Template for displaying Author Search
 *
 * Place this file in your theme
 * yourtheme/simple-user-listing/search-author.php
 *
 */

if ( ! defined( 'ABSPATH' ) ) exit; // Exit if accessed directly

$search = ( get_query_var( 'billing_city' ) ) ? get_query_var( 'billing_city' )  : '';

global $sul_users;
?>

<div class="author-search">
  <h2><?php _e('Search authors by city' ,'simple-user-listing');?></h2>
		<form method="get" id="sul-searchform" action="<?php the_permalink() ?>">
			<label for="as" class="assistive-text"><?php _e('Search' ,'simple-user-listing');?></label>

<input type="text" class="field" name="billing_city" id="sul-s" placeholder="<?php _e('Search Authors' ,'simple-user-listing');?>" value="<?php echo $search; ?>"/>

			<input type="submit" class="submit" id="sul-searchsubmit" value="<?php _e('Search Authors' ,'simple-user-listing');?>" />
		</form>
	<?php
	if( $search ){ ?>
		<h2 ><?php printf( __('Search Results for: %s' ,'simple-user-listing'), '<em>' . $search .'</em>' );?></h2>
		<a href="<?php the_permalink(); ?>"><?php _e('Back To Author Listing' ,'simple-user-listing');?></a>
	<?php } ?>
</div><!-- .author-search -->