First of all, that Doctor Who is Rascist article is a steaming pile of bullshit. Second, their claim that the Doctor telling Martha to "walk like you own the place" to avoid rascism is offensive is also a steaming pile of bullshit, which reeks to me as someone looking for reasons to be offended.
While it's true, a black man may not have as easy a time in Earth's history as a white man, I don't see why the show should have to dwell on this. First of all, on average, how often a year does Doctor Who do stories set in the past? Season 7 had 6 out of 14. And of those 6, only 3 were before the 20th century. So, there's three times a year the Doctor might be in a situation where he might run into hostility based on his skin colour. But really, once the shit starts going down, and it's clear the Doctor's the one with all the answers, I'm sure all the characters will forget what colour his skin is, if it was even an issue for them to begin with.