How to Prevent Events from being added to the Birthday Calendar on macOS
"Add to Calendar" works if another another Local Calendar (besides Birthdays) is present. You can force Calendar.app to have another local calendar, besides Birthdays, by doing the following...
In Calendar.app, go to Preferences > Accounts > and uncheck iCloud's Calendar.
In Calendar.app, create a New Calendar - this creates "On My Mac" group with the new calendar. Add an event to the new Calendar.
Return to Calendar > Preferences > Accounts > re-check iCloud's Calendar.
It will ask to Merge. If an event exists within the newly created "On My Mac" Local Calendar, it will be preserved (otherwise it will be removed).
Now selecting a date within Postbox will add the event to the 1st Local Calendar (non-Birthday).