AFAIK, if a zombie apocalypse or similarly world-shattering event did happen, autistics would be about in the same situation as everyone else. The only ones in severe danger would be the people who can't survive without modern medicine, like those who need seizure medication or those who have other disabilities that need treatment that has become unavailable.
People's reactions to disasters are actually a lot more sensible and a lot less dramatic than the zombie-apocalypse stories that make for good TV or reading. When society breaks down, they tend to team up, hunker down, help each other, and get through it. For example, read about what happened in the aftermath of Hurricane Katrina or during the more recent tsunami and earthquake in Japan. People stayed quite civilized in both situations. Even the "looting" in Hurricane Katrina was overwhelmingly a matter of taking necessities from buildings that would eventually be condemned or gutted before being renovated.
Now compare these situations to a football riot or the chaos of a Black Friday sale--both situations are the product of civilization, and both are much more chaotic and every-man-for-himself than the aftermath of a major disaster.
Why? Well, over our evolutionary history we have had disasters, repeatedly, and those who coped best with those disasters, by cooperating and supporting each other, were the ones who survived. That leads to a tend-and-befriend sort of reflex during catastrophes. People don't panic nearly as easily as you think they might. Consider the reactions of people after the World Trade Center attacks. Look at photos of the event. You'll see shock; you'll see tears; but you'll see very little panic, and you'll see a lot of people helping each other, often helping perfect strangers.
So, in a zombie apocalypse, I think we would paradoxically find that the environment had become somewhat friendlier toward us. We have the ability to contribute, and the same desire to help, as any neurotypical. We can help with whatever work needs to be done; we can help solve whatever problems need to be solved. Just like the neurotypicals around us, we usually have that tendency to want to protect those around us, especially the helpless young. Our social clumsiness may pose a problem, but it's only one of many things that can. One person's got autism, the other's got asthma, a third is mourning a lost spouse, and the fourth is seven years old and can't find his parents. You'll have old people, young people, sick people, and they'll all both need help and want to give help. As an autistic person, you may have a special skill or the ability to emotionally distance yourself, either of which may come in handy. Or maybe you'd be yet another person trying to survive. You might shut down, but you won't be the only one in bad shape. There'll be diabetics who haven't had their insulin, babies and no formula to feed them, injuries with no professionals to treat them. It's scary whichever way you look at it, but I do not think autistics have more to fear from disasters than the average person.