Why only apply your idea of evolutionary logic to fellow animals? We're related to all living things on the planet. "Qualitatively", if we've got nothing on apes then we're no better than any of them, so we oughtn't to kill or harm anything at all. You know why we don't think like that? Because if we ever had, our ancestors would have starved and we wouldn't be here.
I must mention that in your first paragraph, you've made a very sweeping statement in a very small parenthesis. Just consider how much more obviously offensive it would be if you had said, "I would not want to be alone on an island with a black man," or, "I would not want to be alone on an island with a Jew."
I assume you subscribe to the school of thought that because atheists have no absolute authority on which to base their morals, their morals are effectively baseless. I parry, very simply, by saying that in the absence of any moral absolute which we (humans, not just atheists) actually know exists, there are many valid objective bases which serve us well, especially when used in concert. I counter by wondering out loud whether it is worse to be without a perceived absolute moral basis than to use a false moral basis, as in the case of followers of all but one religion (or, of course, all of them).
Back to your actual question: the psychological ability to kill animals and eat their meat has nothing to do with atheism, and little or nothing to do with personal concepts of evolution. Rather it is determined by an effect of evolution: empathy. The more we are able to identify with a creature, the more difficult it is to hurt or kill it. This served us well in the early days before concrete laws, when helping others usually resulted in reciprocation and made everyone happier.
The differences between us and apes are not as important as the similarities between us. In case you haven't noticed, orangutan isn't on the menu at your local restaurants. Neither is dog or cat, for that matter. The idea of killing these animals, or especially causing them pain, makes everybody uncomfortable. That's because we identify with them. Apes on television are eerily similar to humans, and while dogs and cats are more distantly related, in our culture we've come to see them as little friends.
After the most familiar creatures, there's a sliding scale of empathy. We're much more comfortable with the idea of eating sheep and other cattle, but we like to be assured that they were treated well on the farm and were killed humanely. (Contrast this with the religious concepts of "kosher" and "halal", which demand that these animals are killed in ways that cause them brief but terrible pain.)
At the far end of the scale are alien-looking creatures like mosquitoes, which we casually hunt down and brutally murder before they have a chance to feed on us. Once we leave the animal kingdom and consider plants, fungi and bacteria, we generally cannot identify with them at all (for example, we can't understand any mechanism whereby they might feel something like pain) and thus we slaughter and devour them without a second thought for their welfare (beyond working to prevent their extinction).
Those who are vegans for emotional reasons are in that small minority which empathises fully with all animal life, but they still kill their plant relatives. Those on the low end of the compassion meter, on the other hand, might not feel bad about killing even dogs or apes. I doubt very much that this group contains a disproportionate amount of atheists. Perhaps there is some research on the subject.