He is relying on the same data for his assertions as everyone else has been. I see his analysis of that data as no less valid than that of OKCupid, etc.
Blacks do look seriously underrepresented based on the response rates to the two questions. (Suggesting that blacks account for around 4% of OkCupid's users.) That's hardly proof of anything, but it does offer some credence to Coates' argument.
In the real world, it's often very hard to find compelling data, so we sometimes have to rely on compelling argument.
Coates is pointing out that there are good reasons
to suspect strong sample bias.
OkCupid didn't address this -- they just assumed an unbiased sample.
it is at least a plausible hypothesis
Racial views in the US are absolutely filled with (and arguably dominated by) gross misconceptions that seem plausible to many people despite being untrue.