She also believes that the world is run by shape-shifting reptilian aliens who practice mind control from the Moon.
I'm not sure which opinion is more bizarre.
On her blog, she waxes poetic over the book that taught her so much about the aliens:that control our world:
Earlier I wrote that David Icke reminded me of Malcolm X. I was thinking especially of Malcolm’s fearlessness. A fearlessness that made him seem cold, actually, though we know he wasn’t really. All that love of us that kept driving him to improve our lot; often into quite the wrong direction, but I need not go into that. What I was remembering was how he called our oppressors “blue eyed devils.” Now who could that have been? Well, we see them here in David Icke’s book as the descendants of the reptilian race that landed on our sweet planet the moment they could get a glimpse of it through the mist that used to cover it (before there was a moon). No kidding. Deep breath! Yes, before there was a moon! (Oh, I love the moon; can I keep it? Please?). Anyway, there they came, these space beings (we’re space beings too, of course, not to forget that). But they looked…. different than us. And they were.
They wanted gold and they wanted slaves to mine it for them. Now gosh, who does this remind us of? I only am asking. You do the work. Apparently their own planet needed this metal to continue its, apparently, long life. Credo Mutwa, Zulu shaman – and I am on my knees here in gratitude that he held on long enough to tell us about this – calls them the Chitauri, which has become my favorite word of all time (well, of this time that I’m learning all this): my partner and I go around saying Oh, Chitauri, whenever we get a glimpse of one or two of the Chitauri offspring, aka Illuminati bloodline families and their puppets, on the telly. It’s quite the stress reliever, just knowing what we’re looking at. And I like saying “telly” too, because it sounds so English and David Icke-esque. Truthfully our “telly” is our laptops.
It’s an amazing book, HUMAN RACE GET OFF YOUR KNEES, and reading it was the ultimate reading adventure. I felt it was the first time I was able to observe, and mostly imagine and comprehend, the root of the incredible evil that has engulfed our planet. A lot of it is how shall we say: shocking, beyond belief (but not really, if you don’t get too scared), stunning, profound. The deconstruction of language is breathtaking, the interrogation of symbols startling. Magical, in a way. I kept going: Oh, so that’s why…. You will too.
The Reptilian space beings whose hybrid (part human, part reptile) descendants make our lives hell in Paradise were blue eyed devils to Malcolm X, the devil himself to my Christian parents, who never talked about eye color, which I think was not only prudent but wise, although they seemed clear enough about his sex, and as demons in many other religions, including the non-religion, Buddhism, where the advice is often to invite them in until they go away. But maybe these were other kinds of demons. Not the ones controlling not just you, but everything.
Wikipedia summarizes Ickes' theory that enthralls Walker:
Icke introduced the reptoid hypothesis in The Biggest Secret (1999), which identified the Brotherhood as descendants of reptilians from the constellation Draco, who walk on two legs and appear human, and who live in tunnels and caverns inside the earth. He argues that the reptilians are the race of gods known as the Anunnaki in the Babylonian creation myth, Enûma Eliš. According to Barkun, Icke's idea of "inner-earth reptilians" is not new, though he has done more than most to expand it.Walker is of course worshiped by the Mondoweiss crowd. Then again, their grasp of reality is about as tenuous as Walker's.
The Draco constellation from Uranographia by Johannes Hevelius, 1690. Icke's "reptoid hypothesis" posits that humanity is ruled by descendants of reptilians from Draco.
Icke has accused many prominent people of being "reptoids," including Brian Mulroney, George H. W. Bush, George W. Bush, Queen Elizabeth II, The Queen Mother, Al Gore, Kris Kristofferson, Boxcar Willie, and the steering committee of the Bilderberg Group. It is Icke's contention that none of these people are suing him for his statements because they are all, in reality, twelve-foot lizards. 
(h/t Max S)
UPDATE: BlazingCatFur illustrates the theory:
UPDATE 2: On a more serious note, Walker's daughter wrote an extensive essay describing just how sick a human being Alice Walker is.
All this was known when she was honored for her anti-Israel stunts.