My first shorthand solution was to uncheck "Calendar" from Google Account in the OS X Calendar application.
That solves the problem on Mac, but I am 'still' a Chrome user and see these alerts on Chrome too.
There is a long article on Techcrunch from early 2015 complaining about this issue, but a note at the end that Google was working on a solution. No update after that, but I think Google has fixed it now, and you can stop these alerts at the source :
- Go to google.com/calendar, you should see Birthdays under Calendars
- Under My calendars, click on dropdown box to the right of Birthdays and select "Calendar Settings" or "Edit Notifications"
- Select "Contacts only" option next to "Show birthdays from"
- Hit "Save" at the bottom