From my perspective, the American progressive left is deeply distrustful of local / state police, but are more inclined to believe the feds good at least insofar as they enforce good progressive laws against backwards locals. The feds enforcing desegregation is perhaps the root origin of this sentiment. The conservative right on the other hand is very inclined to support local police, but have hated feds with notable intensity, probably sharing the same root but really intensified in the 90s.
For context, I am from here and my parents grew up here
https://en.wikipedia.org/wiki/Albany_Movement
So I had first and second level connections to people who were involved in the civil rights movement. My mom knew someone or knew who knew someone that could get me a call with almost anyone of influence in the Black community nationally. I went to school with a lot of their children - at least the 2nd or 3rd level connections.
The civil rights movement was very aware of things like this at the time
https://en.wikipedia.org/wiki/FBI%E2%80%93King_letter
https://features.apmreports.org/arw/king/d1.html