When a user hides their profile by toggling Hide my public profile in Preferences, their birthday (if they’ve entered one) is still listed in cakeday/birthdays/all. I think most users would expect their birthday to be hidden in Cakeday if they chose to hide their public profile, especially since the Date of Birth field shares a page with parts of the profile that do get hidden.
I was able to reproduce this with a test user account and several accounts that do not have moderator/administrator privileges.