Everytime I check this statement with Cloudflare-enabled sites... it was either always accessible (a nagging screen might be shown momentarily, but that's it), or the block is usually due to that site being a bank or something else that will block Tor users regardless of their firewall solutions. I've just tested it again just in case something has changed, but that statement holds up every time.

Can you please give a non-banking site that a) uses Cloudflare and b) blocks Tor?