My reply should be longer and more helpful, but I'm unable to write clearly right now, so I'll be short but regrettably not nuanced: if it involves other people and shared resources, I don't think you can make it non-political.
If you see politics — not being a politician or partisanship, which have different implications — as inherently bad, you are not seeing politics for what it is; you are seeing politics as some evil process, run by a cabal or by a mob, and your position as inherently logical and reasoned.
This is a bad idea even if you have a good reason to believe you're right. Rumsfeld's "unknown unknowns" are part of why this is a problem.
Let me add a weird metaphor: you are saying smell is something that only comes from perfume, rotten organic matter and certain chemical products. You may not perceive the toned-down smell of things you are surrounded by, like wood, plastics or the air in your office.
This is a good response and I see your point. I don't fully agree though. If someone is making decisions based on their finances, I think it's unhelpful to frame it as "politics" just because there may be some tax implications (the shared resources in your example). If people are moving to a lower tax state to save money, that's not a political decision in my opinion. It's a totally logical financial decision an individual is making.
Now, why I say that this article is political (and unjust imo) is because that very personal and logical decision is being placed by someone else into the realm of politics.
> politics isn't some dirty thing that innately sullies everything and should be avoided.
I strongly disagree with this statement.