I just duplicated this. I downloaded Pale Moon and went to https://hear-me.social/ and clicked on "Register". It puts up a Cloudflare "managed challenge" which loops endlessly when using Pale Moon, but not the other browsers I've tried it with, including Zen, another Firefox fork.
It's a problem, for sure.
You can go to https://hear-me.social/ and click on the register button. This puts up a Cloudflare managed challenge screen which endlessly loops when using Pale Moon. It would be interesting to see if Waterfox has the same issue.