I like using a date of birth of 1 January. It's plausible but also hopefully suspicious how many people seem to be born that day if others do the same.
But if an attacker gets your fake birthday and uses that to successfully reset credentials on another site that uses the same fake birthday?
At some point it becomes your birthday of record as far as the internet is concerned. Doesn’t matter what the actual record says.
Same, my D.O.B. is 1/1/1970 for anything that doesn't justify having the real deal.
I heard from a number of Syrian refugees that this is actually very common in countries like theirs, where births may not be recorded, records are lost or destroyed. Some people don't even know their exact date of birth and they would typically enter January 1st on forms like this too.