I have to admit, I never gave this any thought, until an acquaintance brought it up. I can see it being considered Western, in terms of its politics and culture, but it just seems strange, considering its location.
What do you think?
I’d have to go west to get there, so I don’t see why it wouldn’t be Western.
Yes.
It’s also considered part of the New World.
Everywhere is west of somewhere.
Except the north and south poles
Yes it is, in the way you’re using it, “western” is idiomatic.
They now use the termed “Westernized” so they can include places like Japan.
Outside of Western Europe and Canada and the USA, Israel, Japan, Australia and New Zealand fall into “the West,” even though they aren’t “west” in the traditional sense.
As South Korea, Sinapore and Taiwan start developing, evne more, it’ll be more problematic to use that term. South Korea is the biggest argument now, with some considering it fully developed on par with the West and others saying it’s not quite there but almost.
We have both kinds, Country and Western. 
True poles, or magnetic poles?
Either, provided you use their respective “west”.
You are confusing the definition of First World definition with the Western culture or western civilization definition. South Korea and Japan in no way belong to the latter.
The roots of western civilization are (i) a classical one and (ii) a judeo-christian one.
The answer to your question is yes, Australia is a western country as are most (if not) all former europeans colonies.
So Argentina is not western?
Then y’all know how to dance the Texas Two-step? Cool, who knew?
True Poles and other Slavic people are still considered part of the Eastern Bloc, right? Are Magnetic Poles a seperatist group I haven’t heard about? 
Is the the “No True Pole” fallacy I keep hearing about?
Yes, this, exactly. I’ve never heard of Australia not being considered part of the West.
Morocco is further west than most western European countries, but no one would consider it a western country in the sense that the OP means. It’s a matter of culture, not geography.
Dominated by people of European stock, Christianized, democratic, market economy? Yup, in that sense, it’s Western.
Argentina is as Western as Spain or Italy.
Argentina is a western country.
Could I have 4 fried chickens and a Coke, please?