Political ideologies occupy, in actuality, a very small niche that usually doesn't get in the way of getting business done.
That, um, very much depends. Compare, e.g. Washington, DC in 2015 (where it's mostly true) to, say, St.Petersburg, Russia in 1917 (where it's not true at all). Or, say, Donetsk, Ukraine in 2015 if you want a contemporary example.
Political ideology doesn't matter only where politics don't matter (usually because they are stable, inoffensive, and the society has a general consensus on how things should be done). Otherwise all bets are off -- look e.g. at your own point 2.
I said usually. Of course there are some events in which ideology plays a big part that are going to go down in history. (Strange how the most salient ones, to me at least, seem to come from the totalitarian side of the spectrum.) The quote I was responding to expressed doubts about the possibility of people with different ideologies to work together at all.
Historically, the evolution of government systems was mainly driven by violence, with invasions and revolutions being the principal agents of selection process. The rules of the game were predetermined by our environment - land was a limited resource, for which our ancestors had to compete, if only to ensure the survival of their descendants.
The 20th century introduced a game changer. As agricultural productivity in developed countries rose by orders of magnitude and natural population growth practically came to a halt, possessing a large territory stopped being a necessity. Countries with little arable land, ultra-high population density and no natural resources can now not only feed their population, but also achieve top living standards. These changes may open a fundamentally different route for societal evolution – one that would not be based on violence or compulsion.
A small thought experiment - imagine what would happen if central governments cede most powers to smaller territorial units:
Unfortunately, there are serious obstacles to the successful implementation of this idea:
Do you think these problems are solvable?