HTTPS Everywhere breaks Disqus commenting

When HTTPS Everywhere is enabled commenting on sites that use the Disqus commenting service is not possible, due to the submit button not loading. This problem also occurs on the Disqus blog, for instance at http://blog.disqus.com/post/19805413105/introducing-orbital

The JavaScript console shows the following error message:

Unable to post message to http://mediacdn.disqus.com. Recipient has origin https://securecdn.disqus.com.

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