Better WP Security plugin blocking calls using file_get_contents() method

You shouldn’t use file_get_contents() for remote requests. WordPress does the heavy lifting for you when determining what is compatible on your host.

Instead of file_get_contents() use the following to check for 404s:

$request = wp_remote_get($url);
$status = $request['response']['code'];
if($status === 404){
    //do something
}

You can also use wp_remote_retrieve_body($request) to get the contents of the request.