I wonder whether people who disagree about this are talking at crossed purposes. I think there's politics in a narrower sense (concerning partisanship and state intervention) and politics in a wider sense (concerning power relations and decision making). To depoliticise things in the former sense (by depolarising and deregulating) isn't to depoliticise them at all in the latter sense. In society, arguably everything is economic, legal, psychological, etc. Presumably, what people mean when they say "everything is political" is that politics in the wider sense is both important and on this list.