On my 10.9.x version of Calendars there is another check box besides the one in Preferences.

There is a button that says "Calendars" right below the stop light buttons in the top left of the Calendar window. Clicking this button reveals a list of my calendars (e.g., work, home, etc.) and a check box for birthdays and holidays. See if that does it.

On a Mac since 1984.
Currently: 24" M1 iMac, M2 Pro Mac mini with 27" BenQ monitor, M2 Macbook Air, MacOS 14.x; iPhones, iPods (yes, still) and iPads.