Use the WordPress IXR Client to query a remote XMLRPC method.

my_init_test.php

<?php
  function my_init_test()
  {
    //check for ?test=1 or do nothing
    if(empty($_REQUEST['test']))
      return;
  
    //user id to test
    $remote_user_id = 1;
  
    //load IXR class
    require_once ABSPATH . 'wp-includes/class-IXR.php';
    
    //connect
  	$rpc = new IXR_CLIENT('http://otherwordpresssite.com/xmlrpc.php');
  		
  	//query
  	$rpc->query('pmpro.getMembershipLevelForUser',  'adminusername', 'adminpassword', $remote_user_id);
  	$r = $rpc->getResponse();
  	
  	
  	//show output and die
  	wp_die('<pre>' . var_export($r, true) . '</pre>');
  }
  add_action('init', 'my_init_test');
?>