> Think about how the 'one-drop rule' still applies to whom considers themselves black.
Does it?
> there is a large body of scientific evidence that supports the fact that race makes little biological sense and is mostly a social construct
Given the topic, I'd be skeptical - a large body of evidence might still not be conclusive. However, maybe a more relevant question is why it matters - you are what you might be perceived as, so far it might affect how you are treated.
If that weren't enough there is a large body of scientific evidence that supports the fact that race makes little biological sense and is mostly a social construct. Take the example of the Basque you picked: it turns out the Basque are much different from the rest of people in Europe due to their being (mostly linguistically, but also genetically) the only descendants of hunter-gatherer societies in Europe.
I suggest you read Genes, Peoples, and Languages on the subject: it's really fascinating.
http://www.amazon.com/Genes-Peoples-Languages-Luigi-Cavalli-...