hey Peter,

I've checked in your site, your site user already did configured correctly, if you view their user profile page as guest user or non-admin user, they will not able to see their birthday, you can take a look of my attached screenshot below.

Also you can guide your site user if they would like allow other user see their birthday without birth year, they can only year only them can see it, then set outside to `Everyone` privacy, you can refer on my second attached screenshot.

Hope this help.

And maybe one day you will be able to set year as private by default, if you vote for the following request in Voice system:

Default Privacy for Year of Birth

Thanks for sharing.