I think it's mostly USA and UK where people are afraid of the police by default. I certainly haven't have any problems with them here in Finland.
There are many places in the US where you will have no issues whatsoever from police while in other areas an encounter may not turn out so well.
I'm sure there are similar issues throughout the world if one bothers to look for it.
I would say one difference in the US that's popped up lately is that the increased use of technology in our daily lives exposes the fact that there are many bad apples in the barrel, which makes the whole barrel suspect.
Plus, for many people, the fact that the police tend to style themselves after the military these days tends to worry and bother people.