Being what the OP calls a political atheist is much, much easier said than done. We are being asked if we are capable of thinking rationally about political issues. Most people would believe they fit the bill, but - as we can probably all agree - very few do. It must be concluded, then, that most people who think of themselves as political atheists are wrong. Which ones? Why, everyone else, of course.
We make the assumption that many social and economic issues can be reduced down to quantifiable, individual integers. If (A) is true, then (B) is true. If (A) is not true, (B) is not true. (A)'s true, so easy peasy, problem solved! I wish politics worked like this; I'd be able to liberate my brain from the foggy, ominous mire of ambiguity where most of my abstract thinking seems to wander, held captive by the ruthless overlord that is paranoid skepticism.
In the world of politics, one man's 'fact' is, at best, questioned zealously by an opposing ideology; at worst it is simply someone's feelings held together with enough dogma and loyalty to appear somewhat concrete from afar (I'm not going to cite specific examples because I don't want to derail the thread). For the most hot-button issues, a little patience and resourcefulness will find you a Panel of Credible Experts that will demonstrate, using copious data and exhausting research, the inexorable truth of whatever opinion you might care to have on the matter.
That's not to say that it's impossible to make rational decisions, or to get decent information. We simply have to do so with a respectful nod towards the intoxicating power of ideology and the inherent limits of our own human perception. We must be honest with ourselves about the reliability of the sources we get our information from. We try to be constantly aware of those misleading tricks of logic: Appeals to tradition and novelty, majority and minority, establishment and disestablishment; cherry-picking anecdotes and data; the use of ridicule, and vilification, and association; the strawman, that classic favorite...as well as any number of other emotional appeals or logical shortcuts.
I catch myself all the time...letting my desire for the truth or falsehood of something guide my pursuit and interpretation of information. The best we can do, I think, is to try to be humble enough to acknowledge our instinctive desire for verifying our worldview, and our instinctive fear of cognitive dissonance. These things are a part of the beauty of human nature, but they are not, unfortunately, facilitators of truth.
