Thanks for mentioning that! I took your example and was able to find myself - there was only one record which matched the combination of birth day and state, parents’ ages, and mother’s birth state (which is different than mine). Add in birth weight if you know it, and I speculate you’re almost certain to be able to find yourself.
An interesting aggregation query would be how much information is needed to uniquely identify some large percentage of all births in the data set.
https://cloud.google.com/bigquery/public-data
(Fun fact: I was actually able to find myself in the table based on my birthday, my birth state, my parent's ages and their birth states.)