Outside City Hall, as a nonprofit social justice group was unveiling a report about public safety for Black New Yorkers, Mayor Eric Adams suddenly emerged from the building.

The mayor strode past, a gesture that the nonprofit’s director, Anthonine Pierre, interpreted as a brushoff to her group and the issues it was seeking to highlight.

“That’s right,” yelled Ms. Pierre, who, like Mr. Adams, is Black. “Turn your back like you did on our community.”

Mr. Adams’s first several months in office have been met with mixed reactions, with critics suggesting that his energetic style has not translated into measurable improvements in critical areas like crime, housing affordability and inequity.

The mayor has come under particularly harsh scrutiny from the far left, which has opposed Mr. Adams’s aggressive approach to battling violent crime, a strategy that has included bulking up police patrols and re-establishing roving anti-gun street squads.

Most of the criticism, however, has not come from leadership of institutions associated with the far left like the Democratic Socialists of America or the Working Families Party. It has come from their Black members.

Indeed, several of the leading white progressives in the city, including the city comptroller, Brad Lander, declined to comment for this article.

“I think white people know that they can’t really speak right now against Eric because they are going to look like racists,” said Ms. Pierre, who leads the Brooklyn Movement Center. “Particularly in an age of internet political correctness, I think people who are not Black are very apprehensive about saying anything.”

A prime example arose last month, when passage of the city’s $101 billion budget was preceded by debate over funding levels for the Police Department and school budget cuts. Six no votes were cast, all by City Council members of color, some of whom identify as socialists or are members of the Democratic Socialists of America.

Jeremy Cohan, a co-chairman of the New York City chapter of Democratic Socialists of America, said that at the start of Mr. Adams’s term, his group discussed whether it made sense to be openly critical of the mayor. The answer, he said, is still somewhat fluid.

“Black progressives definitely speak with an air of moral authority,” said Mr. Cohan, who is white. “In politics, there’s shared experiences and shared interests. I think our belief in D.S.A. is that we need political leaders that have both of those things.”

The absence of widespread criticism from white left-wing Democrats in New York is tied to how Mr. Adams has chosen to identify his political roots.

He has long emphasized his lived experience as a Black man who grew up amid challenging circumstances in New York. He says that he has been personally affected by the city’s complex and longstanding disparities, and recognizes how they are deeply tied to racial oppression.

“Here’s a guy that has lived the life of the people who are going through a lot right now,” said Evan Thies, a campaign spokesman for Mr. Adams. “It is real and it is who he is.”

Above all, the mayor says that he has on-the-ground insight on the city’s most vexing problems, and is particularly qualified — far more so than his progressive critics — to judge how best to solve them.

When the federal government threatened to take control of Rikers Island because of violence and mismanagement, Mr. Adams asked for more time to make systemic changes. “Why give me an opportunity?” the mayor said. “Because the people on Rikers, they look like me.”

When the City Hall press corps questioned the mayor about the success of his lobbying efforts in Albany, Mr. Adams pointed out that the reporters who cover him are mostly white.

“I’m a Black man that’s the mayor, but my story is being interpreted by people that don’t look like me,” he said. “How many Blacks are on editorial boards? How many Blacks determine how these stories are being written?”

When the mayor faced questions from Trevor Noah, the host of “The Daily Show,” about the balance between funding the police and funding education and programs that address the root causes of crime, the mayor again shifted to a personal narrative.

He told the story about how his dyslexia was not discovered until he was a teenager, and questioned why Black and Latino students continue to have poor outcomes in spite of the Department of Education’s almost $40 billion budget.

“We’ve been getting played for so long,” Mr. Adams said. “You know how much money is made when a child is dyslexic and is not educated, and he’s incarcerated?”

Charlie King, a Democratic strategist and former head of the state Democratic Party, agreed that Mr. Adams’s rebuttal is difficult for much of the left establishment to challenge.

“He’s been one step away from homelessness and he’s been a victim of police brutality,” Mr. King said. “How many white progressives have been a victim of police brutality?”

Black progressives challenging the mayor don’t have the same problem, said Mr. King, who is Black, because many can cite the same challenges in explaining why they oppose the mayor’s plans.

Candis Tall, vice president and political director for Local 32BJ of the Service Employees International Union, said that she and other left-leaning Black leaders who disagree with the mayor’s crime strategy recognize that they need to “take control of the conversation because we understand our communities.”

She acknowledged that even for them, attacking the mayor is not easy. Black people have been victims of both gun violence and discriminatory policing for decades in the city, and Mr. Adams “is acknowledging that both things exist, which is very real for people, including our members.”

There have been other instances where Black progressives have challenged the mayor. Earlier this month, mostly Black activists gathered in front of City Hall to protest the death of the 10th person in custody on Rikers Island, and to criticize Mr. Adams’s support for solitary confinement.

Mayor Adams, your constituents are dying,” Dr. Victoria A. Phillips, who works with the Urban Justice Center, said at the rally. “You said you represent the Black and brown community, well, step up. Step up and save us.”

Early in the mayor’s term, he got involved in a confrontation with Assemblywoman Latrice Walker of Brooklyn during a state legislative hearing. When she questioned Mr. Adams’s call to toughen bail laws, he hinted that she was out of touch — suggesting that she should solicit the opinion of a recent shooting victim’s mother.

Ms. Walker quickly shot back that the mayor wasn’t the only person qualified to speak on the issue of violence because her 19-year-old brother was shot and killed in the Brownsville neighborhood of Brooklyn when she was not quite 10.

“I know what being a victim of gun violence is like,” Ms. Walker said in an interview not far from where her brother was murdered as tears welled up in her eyes. “I’ve grown up with the with the fear of gun violence.”

Ms. Walker compared Mr. Adams’s crime platform to that of the former mayor Rudolph W. Giuliani, but said it was far easier to criticize Mr. Giuliani, a Republican.

“At least when it was Giuliani, we had a finger to point at him to say: ‘He’s racist and this isn’t fair,’” she said. “But how do you do that when the mayor is a Black man?”

Not every Black progressive leader has been outwardly critical of the mayor: Jumaane Williams, the city’s public advocate and the most visible Black member of New York’s left flank, has had a good relationship with Mr. Adams over the years, and has been measured in how he frames his opposition.

At a City Hall news conference with the mayor in June to announce a “gun violence czar,” Mr. Williams praised the effort but also criticized Mr. Adams’ policy of creating an “omnipresence” of police in the subways. “We are about to go through the fourth or fifth surge of police in the subways and we still have violence,” he said.

Mr. Cohan, of the Working Families Party, said that Mr. Adams’s troubling poll numbers will allow people across the political spectrum to be “more openly critical.”

“What actual improvements of working people and peoples of color lives have you shown?” Mr. Cohan said. “Nothing much to speak of.”

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