Checkbox to make billing information same as shipping information does not work for Anonymous users
Turns out I was kicking myself on this one. I forgot I had some custom hook_js_alter code in my template.php that removes unnecessary js from the page for anonymous users. This was done to improve site speed and because my custom theme didn't require these default Drupal js libraries.

function theme_js_alter(&amp;$javascript) {
  $logged_in_user = user_uid_optional_load();
  if(!in_array("authenticated user", $logged_in_user-&gt;roles)) {
    foreach($javascript as $key =&gt; $value) {
      unset($javascript[$key]);
    }
  }
}


However I do need these javascripts on commerce checkout pages apparently, so I added a request_path() check for checkout and cart pages so the js would not be unset.

I confirmed the My Shipping information is the same as my Billing information checkbox now works for anonymous users.