In this case specifically, I moved the domain away since they want you to pay extra money to use custom DNS servers.
Specifying 3rd party name servers as your domain’s name server was (still is?) not possible with Cloudflare Registrar.
(Disclaimer: I work there)
It's honestly a frustrating problem as we're effectively in an arms race with the likes of Cloudflare, Google et al, and we're in the same boat with less reputable services like scrapers and bots. The recent developments around Web Environment Integrity are concerning to us for the same reasons. Feel free to reach out with any questions or suggestions you might have!
Disclaimer: I work at CF