The site seems broken, accidentally. The way it's using Cloudflare breaks it for any IP that has some high "risk" score in their listing (I.E. any that would be prompted with a captcha before proceeding).
When you use the site you are first asked to fill in a Cloudflare captcha. Once it's successfully filled in Cloudflare assigns you some token in a cookie for the site that you can send with later requests to indicate that you've been previously validated by Cloudflare for access to the site.
However, this site serves at least some of it's content from a second sub-domain
I was wrong, my own testing suggests this is not a firefox bug. Testing on a my own server,
<script async...> tags are credentialed in cross-subdomain requests. This is a bug on their site, and likely not an intentional attempt to stop Tor users.