Disable admin-ajax on the front-end of WordPress sites and cache the resulting 404.

wp-config.php

<?php 
if(
  strpos( $_SERVER['HTTP_REFERER'], 'wp-admin' ) === false &&
  strpos( $_SERVER['REQUEST_URI'], 'admin-ajax.php' ) !== false
) {
  header( 'Cache-Control: max-age=30000, must-revalidate' );
  header( 'Expires: ' . gmdate( 'D, d M Y H:i:s', strtotime( '+5000 minutes' ) ) . ' GMT' );
  header( 'Last-Modified: ' . gmdate( 'D, d M Y H:i:s', strtotime( '-5000 minutes' ) ) . ' GMT' );
  header( $_SERVER["SERVER_PROTOCOL"]." 404 Not Found" );
  die;
}