I for one want to offer a heartfelt apology. As someone that works in this space, bots are becoming more and more sophisticated. I can't speak for Cloudflare, but we're definitely not interested in your personal information. As someone who also prefers their privacy on the web, the fact that bot signatures overlap with privacy-centric signatures sucks. I myself have experienced it on my mobile device with Ghostery. It's frustrating, I know.
Would you mind sharing the guide you used for hardening your Firefox? I'm curious to see what could potentially be triggering the issue.
Also, I just want to say, I think it's hilarious that a site blocked you but then allows you to continue browsing after changing your user agent. That right there is bot behavior.
To circle back around to the actual block, I bet changing your skin executes JavaScript which flags something from the anti-bot software.