People will of course choose privacy over no privacy with all else being equal, but privacy is the first thing sacrificed when push comes to shove. If the average person is given the choice of having everything said within earshot of their phone being recorded and sent to Facebook or giving up Instagram, they'll happily choose Instagram and forsake their privacy.
If privacy advocates want to start turning the tide in this battle, the first step needs to be convincing the average person why privacy is important on a personal and tangible level. No arguments about future totalitarian regimes or hypothetical ideals. Abstract concepts like that rarely motivate people who have so many more practical political concerns. It needs to be something that is more important to people than having access to Instagram. And I have absolutely no idea how that could be accomplished which makes me concerned that we're already too late.