Heya Acid!
I believe Xenforo is set up so if you tick the 'Show Age' it will show your age, but not your Birth Date.
It will still show on the Birthday Tab that it's your Birthday today, but it won't show your age or Birth Date.
I also believe if you have your birthdate not shown to anyone, it won't list you on the birthdays' tab (Don't take my word on this).
Just going to go over what I said above with an image to make it clearer. Tick the top box, it'll show your birthday and month; not your birth year (MM/DD/XXXX - X is nothing shown). Tick the bottom box, then people can see your age (as shown below it). You cannot tick the bottom box with the top box unticked.
Any other questions, just quote me and I'll try my best to find the answer for you! Cheers,
Jash