In order to work properly the prolyfill needs access to the stylesheets on the page. If a stylesheet is served from a different domain it needs to have a CORS header, e.g. Access-Control-Allow-Origin: *. You can find more information about how to enable CORS on your server at enable-cors.org.
For better performance it’s also recommended to use the attribute crossorigin="anonymous" for cross origin <link> tags:
<link crossorigin="anonymous" href="http://example.com/styles.css" rel="stylesheet">