The general impression from talking to people who live then (I was a baby in the 1970s so I knew/know a fair number). The violent groups were looked on as weird or kids who needed to grow up - they were ignored for the most part other than cheering on what the police did.

There is a reason Rosa Parks was chosen to start the bus boycott - she comes off as "just like me" to the average person. Thus when she couldn't take it anymore the rest of America didn't write her off.