Finally!
I thought I had the answer below but by the time I finished writing it I noticed the problem was back. You can try it, but it just deletes the Birthdays temporarily.
There must be a problem with iCloud pushing it to the Calendar/Notifications. Has been no way for me to turn it off thus far. Another thing Apple needs to fix ASAP.
Even after deleting the Facebook app, it still does not work. For me, the only way it will work is to delete the Birthdays from the iCloud Contacts (merged from Facebook), but there is no way i'm doing for each individual contact...
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Ok, I've tried a bunch of things and this is what worked for me.
First do some of the things listed above i.e...
1. Settings/ Mail, Contacts, Calendars; turn off all calendars and Contacts in all of your accounts. It will ask you if you want to delete from phone, yes, do that too but be sure to have everything backed up in the Cloud first. Next go Default Alert Times and set it to None.
2. Delete the Facebook app.
3. In the Facebook Settings: turn off Contacts and Calendar.
Ok, now there should be no birthdays in your Calendar or in the Notifications pull-down menu. If there are birthdays there, then you probably didn't turn something off.
4. Now, Reinstall the Facebook app but do not turn on your Facebook Calendars or Contacts. Unfortunately this means you can't sync your Facebook Contacts with your iPhone.
5. Go back to Settings/ Mail, Contacts, Calendars. Turn on Contacts and Calendars.
You should have just about everything you want except Birthday notification.
This has worked for me when nothing else did. I'll check back to see if it worked for others.
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Again, did not work for me, but may be worth a try for others setup differently.