How can I get rid of duplicate birthdays on Calendar?

You may be seeing a combination of birthday events that you have manually entered in Calendar and birthday info that is shared from within the Contacts app.

If you wish to suppress viewing the bday data from Contacts, click Calendars in the upper left corner of the app and then uncheck the box for Birthdays listed under Other.

If you prefer to see the data from Contacts only, then you'll have to pick and choose those manually entered birthdates you wish to delete from the Calendar app.