If a 'normal' organisation is able to take over these roles, this organisation becomes a defacto government and most people won't resist it, as long as they are able to live within the system. People's revolutions are relatively rare in the grand scheme of things.
I should have mentioned that the reason most people don't resist government isn't simply that resistance is futile (in the way a person likely won't resist a mugger with a gun), but rather that they don't feel like they are being wronged at all.
That's a good point. In countries like France and Canada, that's how sharia works. For the people who accept it, it becomes a de facto alternate government (officially, subject to the laws of the land in which it operates, but in practice, a law unto itself).