I delete any application that requires all-or-nothing location privileges; if Uber acts this way now I'm done using Uber.
Being able to make it such that location services are an all-or-nothing proposition when there is clearly support for "only when using" in iOS annoys me to no end. The fact Apple doesn't do this is what is actually alarming, given their stance on "privacy".
This is the calculated risk Uber is taking. Presumably they believe that they will only lose a tiny sliver of their user base over the all-or-nothing approach. Now that they're well past the "early adoption" phase in many markets this is a "smart" corporate play.
I doubt they'll lose even 1% of their installed userbase over this change.
It's now more convenient to use competitors apps, though, and i haven't actually used uber since the change.