I was thinking about that the other day. The difference here is, in part, the police had been making a number of "symbolic arrests," as reported in the news, rather than straight up arresting people for prosecution, whereas back in MLK Jr.'s day, they were truly risking their freedom. Add to that, they were blocking city streets that could then be avoided. While blocking a city street will create an inconvenience for people, it will not create a 90-minute delay due to blocking a major interstate highway in the middle of rush hour traffic.
Also, the protests happening now are against a group of specific people deemed to be harming another through direct action, not against a system design with the intention of creating second class citizens. Far too many of us know officers who are working honestly, trying to be of true service to the communities employing them. Add to that, with the backlash seen against the police - snipers in Dallas and insults and verbal threats hurled by protestors - today's protestors come off as having less gravitas than those working with Dr. King. Those sorts of things were going, to a lesser degree, fifty years ago, but the movement had a defined leader denouncing such actions, calling for peaceful protests and a specific goal. Today's protestors have no great leader speaking out for peaceful resolutions, instead they just come off as an angry mob. The only leaders known to the nation at large have been highly suspect in their character over the past twenty or thirty years (Al Sharpton, Jesse Jackson, etc.), and the only calls for peace coming from the afflicted group are from random people showing up on the news, drowned out by the violence that's already happening.