BALTIMORE—For the Rev. Donté Hickman, the recent spurt of violence in his church’s East Baltimore neighborhood—where six people have been killed since April—is disheartening.

“We thought we ended the fires that were burning, but those fires have turned into gunfire,” he said, referring to riots after the 2015 death of Freddie Gray from injuries the 25-year-old man sustained in police custody.

While...