Please note, that currently - there is no option to turn of the notifications about specific family events.
However , in this case, I can suggest you the following: if you'll enter the birthdays dates for those individuals in "free text" format on their profiles - and then enter the dates manually - the birthday won't show up on the calendar and no notifications would be sent- but the date will appear on the profile details for each person.
In order to enter the date in free text, please go to the individual's card in the Family Tree Builder program > click on it twice to open it > click on the calendar icon next to the date line > in the "type" section, please choose "date in free text" > insert the date manually > save > re-publish the updated project to your family site.