I know that in theory there are non-skeptical atheists. If you don't believe that any personal god exists I suppose you could in reasonably good conscience call yourself an atheist. When I was posting at the Internet Infidels Discussion Board, we accepted deists and pantheists as "freethinkers" and "infidels" as a matter of policy. One could also, I suppose, say that Scientologists and reincarnation-friendly Buddhists count as atheists. One could even, I guess, say that a dogmatic Marxist might be an atheist because Marx proclaimed atheism as part of communist dogma. (I must hasten to add that although I have some pretty sharp disagreements with a lot of my fellow communists, many of them quite radical, I've met very few actual communists who actually behave dogmatically, and all of those were decidedly marginal.)
The thing is, though... I don't actually know anyone like this. The people who go to the trouble of self-identifying as atheists, the readers of my blog, the contributors to atheist discussion boards (when I was participating), the members of atheist Meetup.com groups: these people are thorough skeptics. They did not wake up one day and decide no god exists and construct a "worldview" or even a social life around that decision. Rather, they decided to think skeptically about the world, and applied that skeptical thinking to their beliefs about god, and came to the conclusion, perhaps inevitable, that no god exists. There are a few exceptions, people who happen to believe that no god exists but are not thoroughly skeptical, but I've noticed a tendency of such people to fall (or get pushed) away from the community of self-identified atheists. While it's certainly logically possible to be a non-skeptical atheist, they are at best only marginally represented in what passes for the "atheist community."
Even people who succumb to various forms of "retail" non-skepticism, people who accept one form of "junk science" or another because it supports one deeply-held belief tend to fall away. I had a conversation the other day with a person who was profoundly opposed to the legalization of marijuana. She offered as "evidence" the fallacy of reverse causality (most of the fucked-up people she knew smoked marijuana); when I pointed out the fallacy, she retreated into the odious "we all have our different
In contrast, my own communism is reasonably well-received in atheist circles. Communism is not a mainstream opinion in atheist circles; atheists are by and large reasonably moderately prosperous middle-class people against whom the capitalist system has not (yet) unleashed its awesome power to completely fuck over. I have some advantages: I'm reasonably competent at constructing and expressing skeptic-friendly arguments. I don't of course receive instant acquiescence, but most everyone listens respectfully, asks good questions, quickly abandons obvious myths, and immediately concedes minor points. It doesn't hurt that I'm willing to concede errors of past communists.
The community of self-identified atheists is composed not just mostly of but predominantly of skeptics, and they are skeptics in every sense of the word: they subject beliefs to critical scrutiny, including their own. These are people who don't just have the "right" opinions, they consistently employ the "right" methodology to evaluate their opinions. It is bad to exempt an opinion — any opinion — from skeptical scrutiny. Skepticism is not just something that atheists happen to enjoy, they consistently display a moral duty to subject their own opinions to critical scrutiny, and they try to impose an ethical obligations on others to subject their opinions to the same scrutiny.
"Atheist" is as much or more a matter of self-identification as it is a purely descriptive term. Indeed, most of the people I know who do not believe any god exists but do not believe that all beliefs should be subject to critical scrutiny do not self-identify as atheists. They at most self-identify as agnostics; they usually do not include their religious beliefs or their epistemic methodology at all in their self-identification. People who actually do self-identify as atheists are almost always skeptics, and non-skeptics who "try on" the atheist label rarely last long in the community, and only the most stubborn hold on to the label. So no: They may be agnostics or non-religious, but such people should not in any practical sense be considered atheists.