That's enough to identify people in some zipcodes.
https://www.johndcook.com/blog/2018/12/07/no-funding-for-unw...
https://www.johndcook.com/blog/2018/12/07/simulating-zipcode...
I don't see any reason to give them your exact birthdate.
They could obviously dig into the billing data and get my info, but at least it's not right there together.
That's enough to identify people in some zipcodes.