I've tried raising this issue on their forum, where I've failed to get the attention of the engineering teams, and while posting the ray ID should be sufficient, all you'd really get is clueless, unpaid volunteers asking you questions in circles like "what website do you see this on" (everywhere), "are you using adblock" (no, and Adblock has never blocked their Turnstile scripts) and "what's your user agent?" (the default Chromium one).
If I had to hazard a guess, it's their bot management script seeing "Linux" in the user agent and detecting missing video codecs (which is par for the course for standard Chromium builds), and thinking it's a headless browser. Between the the fact that differences between the JS runtime of Chromium and Chromium headless are very small these days, and the ClientHello permutation has destroyed bot management vendors' ability to distinguish different browser builds, they decided blocking all Linux users using Chromium was fair enough.
I get that it's a frustrating situation but you're viewing CF in the worst possible light ("trying to lock out Linux users" assumes an intent not on display) and I think it's counterproductive to success.
(I have no doubt ypu are seeing the problem on your PC; but generalizing a single point to all Linux users just screams "technical incompetence" and makes me want to ignorw the post)
For an issue that pointed to cloudflare, but ultimately was our hoster having an issue with completing the TLS handshake...
After infra update ofc.
Tldr: had the opposite experience, for a technical issue :)
Works for me on Linux in Firefox and Chromium.