Isn’t that for births only?
What leads you to think that the list applied to parental race as well?
Can you find ‘Caucasian’ on that list?
Birth certificates are handled by the bureau of vital stats.
Vital stat laws apply.
Otherwise the birth data is useless for statistical and census reasons I should add.
Of course, that hasn’t stopped any kind of stat manipulation in states like, oh, Illinois where the recently departed vote year after year.
*cough*
[Or New York with Motor Voter!]