Do you feel angry, defensive, threatened, annoyed, or aggressive when you think about politics? Then you might be an ideologue. Do you feel curious, compassionate, thoughtful, surprised, or playful when you think about politics? Then you might not be an ideologue. Personally, my intuition is that a conversation in most any domain, politics included, with a curious thoughtful person is likely to be much more productive than a conversation with an angry, defensive one (where productivity is defined as learning what the truth is).
Rather, if someone describes himself as "non-ideological" that generally means he's bought into his ideology so strongly that he no longer perceives it as an ideology.
I know nothing about Australian politics. Am I allowed to refer to myself as non-ideological when it comes to Australian politics? Or do I have an ideology regarding Australian politics that's so strong that I don't even perceive it as an ideology? ;) [winky face is supposed to put you in a curious, playful mindset ;)]
To take my point even further: do I have an ideology regarding the best way to use a bucket full of Legos? What is it about politics that causes everyone to have an ideology a priori? It sounds as though you think that thinking about politics the same way I think about the best way to use a bucket of Legos is somehow ruled out by definition. Would you say that's an accurate summary of your position?
Do you feel angry, defensive, threatened, annoyed, or aggressive when you think about politics? Then you might be an ideologue.
Or, you might be someone who has values and recognizes that the political ideas of others harms those values.
Politics as gymnastics for rationalists. No one one Less Wrong is quite sure why politics is a taboo topic or how things got to be that way. What we do think we know is that politics is a great way to bring out the irrationality in people. So why not take advantage of that and use politics as a way to measure rationality? Since politics brings out the most irrationality, it should provide the strongest signal. Since there aren't useful objective metrics of how a political discussion went, we'd have to use subjective judgements by neutral third-party raters, kind of like they do in gymnastics. (In the comment thread for this post, feel free to find fights that you have no dog in, improvise a rationality rubric, and grade participants according to your rubric... let's see how it goes.)
Be a sheep. This is probably the exact opposite of what you were taught in your high school civics class. But if my friend Jane is more intelligent, more informed, and less ideological than I am, it seems like voting however Jane is going to vote is a strict improvement over voting however I would naively. It also saves me time, and gives Jane an incentive to put even more time in to carefully considering political issues since she now controls two votes instead of one. Done on a large scale, this could provide an interesting twist on representative democracy. Imagine a directed graph where each node represents a person and an edge is directed from person A to person B if person A is auto-copying person B's votes. There's a government computer system where you can change the person you're auto-copying votes from at any time or override an auto-copied vote with your own personal guess about what's best for society. Other than that, it's direct democracy... all bills are put before all citizens to vote on. Problems this might solve: