> Update #3

> If you care about your unlisted URL privacy with Cloudflare, make sure you don't have the Crawler Hints feature enabled. - A good hunt, thanks and sorry!

How about not using CloudFlare at all?

Quoting from CF's own blog [0]:

> Going forward, because the benefits are so substantial for site owners, search operators, and the environment, we plan to start defaulting Crawler Hints on for all our customers.

Which by the way directly contradicts what jgrahamc stated in this thread.

[0] https://blog.cloudflare.com/crawler-hints-supports-microsoft...