Intentionally, this should not work. As referred to before, spoofed and fake User-Agents can and should be challenged by Browser Integrity Check.
Browser Integrity Check has methods to make sure that your browser is actually what you’re saying it is - and if it decides that you’re lying, you should fully expect to receive a challenge page.
Edit: to clarify, here is an example. It is fully expected that I will be stuck here (and I am) since my User-Agent isn’t truthful.
Be that as it may, the supposedly improper web standards are supported by all mainstream browsers and hence don’t have any issues.
Whilst we might have differing opinions on what should and shouldn’t be a standard, that isn’t a decision that can be made by a single browser. We wouldn’t break the internet for the minority of internet users, would we?
As per Browser Version Market Share Worldwide | Statcounter Global Stats, Samsung Internet 16.2 is vastly more popular yet makes up 1.94% of the collected user agents. This is without going into the specifics of how often this ‘Pale Moon’ browser will be seen on the internet.
A browser that is intentionally deviating from how the rest of the common browsers works cannot expect to receive the same level as support - especially when delving into years and years of patching an EoL base (ESR 68.0) that was created by someone else (Mozilla).
The browser is saying it’s Firefox - and it isn’t - and should expect to be challenged on that.
We should agree to disagree - but there is no arguing that if an edge-case browser is having issues due to their own development philosophy, they should be the ones who get up-to-date with almost 3 years of changes in Firefox.
https://support.cloudflare.com/hc/en-us/articles/200172476-Contacting-Cloudflare-Support is the only way to contact Cloudflare support - if you do not have a zone then you are not a customer of Cloudflare, so there is no obligation of support being available to you.
The site owners whose websites you are having issues with however are a customer of Cloudflare - that’s why it’s recommended you report it to them and they can go through the proper channels.
There is no way for you to get in direct contact with technical support without a paid plan, so please defer that task to the site owners who will be able to do that for you.