I'm stuck in Cloudflare loops as well, been a week or two. It works in "Private" windows so I'm guessing it's an addon. I think it might be either uBO, Privacy Badger, IDCAC (fork), or DecentralEyes.
Technology
A nice place to discuss rumors, happenings, innovations, and challenges in the technology sphere. We also welcome discussions on the intersections of technology and society. If it’s technological news or discussion of technology, it probably belongs here.
Remember the overriding ethos on Beehaw: Be(e) Nice. Each user you encounter here is a person, and should be treated with kindness (even if they’re wrong, or use a Linux distro you don’t like). Personal attacks will not be tolerated.
Subcommunities on Beehaw:
This community's icon was made by Aaron Schneider, under the CC-BY-NC-SA 4.0 license.
It's the opposite for me, private mode causes more Cloudflare prompts (and Google captchas).
I basically can’t have anything running for privacy anymore without Google capchas triggering. It’s driving me crazy. 
Most work with microsoft edge, but i don’t know if the others worked with edge before.
The fact you say "most" and not "all" suggests this isn't a FireFox problem. Also, given how popular Cloudflare is (30% of global web traffic?) I'd bet if there was something incompatible it would be fixed. Immediately.
Yes, that makes sense.
I haven't experienced this yet and I've been on 116 for 1-2 weeks now. Can you post some sites that you've had the issue with so I can see if I have the same problem? The only extensions I run are uBlock-origin, dark reader, and react dev tools.
Actually i don't remember all, since i followed links from other sites. Others i found a workaround. The only one i tried to make work and still can't is suprfit.com.
That site is working fine for me. Maybe it's a difference in privacy settings? I'm just using standard mode's default.
That's the site not working in microsoft edge neither. I just tried the troubleshooting mode in ff, still the same. It does work with ff on mobile though. Luckily i ordered my new kettlebell last week when it still worked, gonna take a while 'til i need a heavier one :)