I just started having this problem too. I use Google Chrome for my web browser. I tried it again inside a Chrome Incognito Window (similar to a Safari private window), and it worked fine. Is there some setting or cookie that could be causing this problem?

Following up on my previous comment... From the site settings page in Chrome (chrome://settings/content/all), I deleted all site data and permissions for apple.com. I next went back to the Cloudkit dashboard page and refreshed it, but I still got the error message. So I pressed the "Sign out" button there, and then signed back in. It is now working again for me from a regular (non-incognito) Chrome window.