They never claimed causality.

And they also state at the end of the article that they do not have a representative sample of the population.

But if you do use the website and surf through some profiles, it becomes pretty clear that the majority of the users are, as the article states, younger, more educated, and more progressive than the average American. I would go even further and say that the vast majority of the users would not self-identify themselves as racist.

Now question for OKCupid would be, wouldn't it be interesting if you could make a table showing the relationship of race to socioeconomic status, and then the breakdown of reply rate by socioeconomic status?

You say, "they never claimed causality," but they say, "Your Race Affects Whether People Write You Back" and "racism is alive and well".

For example, here's an alternative explanation consistent with their data:

Perhaps black females are generally more solicitous, and send out lots of communications, being generally non-discriminatory about who they communicate with. This would explain both their own high reply rates and their recipients' low reply rates.