Again do you have any evidence anyone at all listed their race as "African"? I understand what you're offering as opinion, but I'm more interested in evidence.
Does the race the mother gives appear on the birth certificate issued to the family and the record kept at the clerk's office even if it doesn't fit into pre-established categories? I don't know. I haven't seen enough birth certificates.
In some states at around the time Obama was born, the clerk or the state might simply reject what the mother said. But in others there might be a discrepancy between the record for the family and the record given the state health authorities.
So, yes, until I see more birth certificates, it's more of a gut feeling, but I don't think a Hawaiian clerk would have rejected "African" as a racial label. And that would stay on the birth certificate, though the information would be recoded when it was compiled for official statistics. But I'd have to actually see examples to be sure of what's more of a hunch.
Nowadays only 5 states still list the race of the child on birth certificates. Hawaii is one of them.
In censuses you can give your race as you like. It either gets recoded as one of the government categories or as "Other."