I know nothing about Australian politics.

Yes, you do. I assume you're at least aware that it's a parliamentary constitutional monarchy with norms resembling those on other advanced western democracies.

Am I allowed to refer to myself as non-ideological when it comes to Australian politics?

You have an ideology about how governments ought to work, you may not know enough about Australia to know what its doing wrong or which party is closest to pushing things in the wright direction, but if you did the research you'd either find yourself sympathizing with one of them or conclude that all of them are insane and advocate some radical (from the point of view of internal Australian politics) position that hardly anyone there is advocating.

Let's replace Australia with something like Saudi Arabia, North Korea, Belarus, or Kazakhstan. I'm guessing you probably know about as little about at least one of those countries as you know about Australia and yet you probably have opinions about what's wrong with those countries.

To take my point even further: do I have an ideology regarding the best way to use a bucket full of Legos?

You have priors and preconceptions about it.

What is it about politics that causes everyone to have an ideology a priori?

Because the word "ideology" is generally used to refer specifically to politics.