The book was written by a consortium of 23 academics and bloggers, primarily Americans, partially Australian, and with only a few Brits. The fact that a bunch of non-British folks are bitching about a British show lends them precious little credibility to begin with. Add to that that they're academics and feminist issue bloggers, I just really don't think the book should be taken seriously.
If they wanted to bitch about NCIS being racist, by all means, but Doctor Who? Sorry, not your country folks. STFU/GTFO.
Just to clarify: your argument is that "academics" ought never to be taken seriously? Is that your real opinion? Not only is that an ad hominem fallacy, but it's a damned bizarre one. Martin Luther King Jr. was an academic. Most of the major movers and shakers in the feminist movement of the 70's (a movement that every woman on this BBS board is living the fruits of) were academics, and "feminist issue" people. The people who are (hopefully) eventually going to save this planet from climate change extinction are going to be academics. Since this is primarily a science fiction board, allow me to point out that many of the best science fiction authors of all time were / are academics. I'm just saying - it was a very strange comment for you to make. (Perhaps I misunderstood?)
Anyway, the attack of racism on Doctor Who would certainly be very true decades ago. Talons of Weng Chiang is the most obvious example, but there are others. And, as has been pointed out, the RTD era was actually very good about showing equal representation, at least in terms of black people. Not living in England, I honestly have no idea whether other minorities are not being equally and fairly represented, but in terms of black representation, I have absolutely no complaints. (Compare to an American show, say, Friends, which took place in New York City, for God's sakes, but had about 99% white people - awful, just awful.)
Now, as for sexism in Doctor Who - that's a different story entirely. There's an issue that BBC and Moffat should really do some soul-searching about.....