But other early voters cited the rising crime numbers: As of June 6, shootings in New York City had risen by 68 percent from last year; homicides had risen by 12 percent over the same period. Fears of violent crime have led some leaders in predominantly Black neighborhoods to reject efforts to defund the police, highlighting a divide that cuts across racial, ideological and generational lines. “I would like to feel safe walking down the street,” said Barbara Mack, a retired guidance counselor who voted for Mr. Adams on Saturday in South Jamaica, Queens. “He’s been a police officer,” Ms. Mack said. “He’s supervised police. He’s tough. I don’t think he’ll accept garbage.”