Cops experience professional deformation. Most of the other humans they see at work have been bad or have been involved in something bad. This eventually has an effect on anyone. It's not a good effect. They start to expect it in other people, they start to assume the only folks they can trust are the ones they usually see doing the "right" thing (other cops). This turns them into bad people.

The effects only get more pronounced in a society where literally every lunatic could have a gun and could therefore murder you at the drop of a hat. Trusting a strange situation will mean your death, eventually. It's inevitable.

This is therefore not a matter of distrust, because you don't need faith or trust to know certain things about the transformative effect this would have on people. They live under mortal threat every second they're outside in uniform. They're going to be monstrous.