crmURL and async JS requests do not preserve https and are blocked by browser

Upon setting up a profile form with a country and state drop-down, the country drop-down issues a request to load the state values when a country is selected. If the page is loaded over https, the request is made with http, leading to the following error:

XMLHttpRequest cannot load http://DOMAIN/membership-information/?page=CiviCRM&q=civicrm/ajax/jqState&_id=country-Primary&_name=country-Primary&_value=1012. No 'Access-Control-Allow-Origin' header is present on the requested resource. Origin 'https://myelitis.org' is therefore not allowed access.

We invoke the form as follows in a Wordpress post.
[civicrm component="contribution" id="12" mode="live"]