I've honestly only experienced the opposite; their captcha is reasonably easy to bypass, and I've successfully automated access to a few sites "protected" by the Cloudflare captcha (behind a VPN, no less).

> I use a heavily customized Firefox config on Linux.

If you really care about privacy, you should blend in to look like everyone else. Avoiding being tracked raises alarm bells. You have to let them track something; but no one ever said it had to be you.