This is almost certainly a firewall rule put in place by the operators of that site. My own sites which are protected with Cloudflare do not exhibit this behavior when using Firefox.
Privacy preserving extensions like uBlock Origin, Canvas Blocker, Decentraleyes etc. used in Firefox also trigger the CloudFlare wall of harassment. Some of the actions of these extensions prevent browser fingerprinting and CloudFlare gets easily confused when this happens and unnecessarily triggers a lot of challenges for a user. You can easily get sucked into the blackhole of captchas - sometimes even solving 5+ captchas isn't enough to convince them that you are a real human.
I used to work there, and there wasn't a global "do this for this browser" (except for a little bit to reduce annoyance specifically for the Tor browser).
It is almost 99% certain to be a site operator firewall rule based on the browser user agent. This may even be accidental, they may have been hit by an aggressive bot using a UA string that matches Firefox and the site operator may not even realise they've done this (if they use Chrome, which is likely).
Is there a meme like name along the lines of "self-own" when you go online and have a tantrum about someone doing something to you only to find out it's your own doing that caused the issue?
