Except the part where he showed up without guns. I think you missed how they won sympathy...
MLK was non-violent, but the bystanders weren’t. They threw rocks and other things at the police.
People not trained in non-violence saw what the police and firemen did to the protestors in Birmingham in newspapers, magazines and on TV 50 years ago and they became violent.
It has been said that non-violent civil disobedience leads to violent civil disobedience.
Whatever methods of resistance people choose, the outcome may not be very nice.
The sympathy among the white population was extensive in the early 1960’s but faded as the violence in the aftermath of the non-violence spread across the cities in the North.
Conservatives of the 1960’s like author Lionel Lokos were critical saying that violence always seemed to follow the non-violence.
He penned a book published after Dr. King’s death entitled “House Divided: The Life and Legacy of Dr. Martin Luther King”.