You know, repeating the same tired stuff over and over doesn’t make it true.
That is for the health statistics that are submitted to federal authorities. They are "coded" in accordance with federal categories. The birth certificates that parents recieve for identification purposes aren't under those regulations.
If you look at Hawaiian censuses from territorial days, "races" included Hawaiian, Part-Hawaiian, Caucasian, Chinese, Japanese, Korean, Negro, Puerto Rican, and Filipino. Given all those possible answers it wouldn't be unheard of for a clerk in Hawaii in 1961 to put down the father's race as "African," all the more so, since there were so few African-Americans in Hawaii at the time. I'm not saying that's what happened, just that such an answer on a birth certificate doesn't automatically make it fraudulent. Hawaii just wasn't as strict about these things as some other states.
That fact alone does make it a forgery but there are several other irregularities of a technical nature.
"Real" and "fake" can be hard to sort out, since the document in question isn't an original 1961 birth certificate, but a more recent computer generated birth certification. So whether it's real or not, it's a copy.
But it's not even that, really. Most of the discussion centers on computer graphics posted online, not on an actual document. And there are probably more than one graphic out there. Some of them are fake. I don't know whether all of them are.