Dear Joseph,
The North Carolina Birth Index I mentioned is indeed at Ancestry.com.
I did not see any presumption about race at all in the listings. I think race was left out entirely. I assume that much information was left out to prevent identity theft, as many of the people listed are still alive.
That being said, I found birth information and the name of one, sometimes two, parents for over 50 people I was looking for. I found it very helpful indeed.
I am sorry it did not help you in your search. I hope that you have much sucess in the future with your research.
Sincerely,
Lee