Another alternative... with no helper columns....
This formula in F1 counts total records that have month from drop down in either the Birthday or the Anniversary or Both.
=SUMPRODUCT((TEXT($C$2:$C$10,"mmmm")=$G$2)+(TEXT($D$2:$D$10,"mmmm")=$G$2))-SUMPRODUCT((TEXT($C$2:$C$10,"mmmm")=$G$2)*(TEXT($D$2:$D$10,"mmmm")=$G$2))
This formula in H2, begins to extract the matching information and pulls only the number of records indicated by the formula in F1:
=IF(ROWS($A$1:$A1)>$F$1,"",INDEX(A$2:A$10,SMALL(IF((TEXT($C$2:$C$10,"mmmm")=$G$2)+(TEXT($D$2:$D$10,"mmmm")=$G$2),ROW($A$2:$A$10)-ROW($A$2)+1),ROWS($A$1:$A1))))
the above formula is an array formula and must be confirmed with CTRL+SHIFT+ENTER keys instead of just ENTER.. you will see { } brackets appear around the formula...then copy it down as far as you want and across the other relevant number of columns.
If you adjust the ranges to suit a large database, you will need to reconfirm the formula with the CSE keys and then copy down and across again.
See attached.
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