Everything is fine - until someone complains.
Yes, my test install of MLS "Directory of Members' does list birth days (and for children birth dates) by default. However due to the number of pages, I don't think most units pass that out to the general membership. The Abbreviated Directory is the one usually handed out en mass. it doesn't have birthdays. To date, I haven't noticed birth days listed in the on-line systems for most members.
But if you're looking for policy, you might want to look at
Handbook 2, 21.1.15. As always, the Bishop and Stake President hold the keys to interpreting those policies.
But as I pointed out, the real problem is keeping the system up to date. A system that could leave someone out risks hurt feelings. Usually this is brought up due to a non-member who attends youth classes, but there's any number of situations that could arise.
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