Is Anubis a DNS service? I was under the impression that it was basically just a reverse proxy that you ran, which required a proof-of-work before it would pass the request off to your various services. If that’s the case, it’s doing a fundamentally different job than CloudFlare is. Because the DNS will likely hit CloudFlare before being forwarded to your Anubis. Like the order of the request would be:
User>CloudFlare DNS>Anubis>Site
If that’s the case, using Anubis wouldn’t change the fact that it’s being blocked by CloudFlare.

If Anubis is an actual DNS service, I may need to look into it more for my own use. I hadn’t bothered, because I thought it was more like Nginx.