The error message was fairly self explanatory: it mentions the restriction was on the Build Plan object, not the Differential revision (if you view it in private/incognito mode). In Phabricator, various objects can have their own policies. Objects can be attached to others, like builds to diffs. Diffs had been set to be public on creation, but for some reason, all the Harbormaster build plans required 'All Users' to view them, which requires a login.
I've fixed this by changing all the build plans to be public, which they should have been in the first place.