When Mayor Michelle Wu cracked down on outdoor dining in Boston’s congested North End neighborhood last year, appeasing residents beleaguered by crowds, trash and blocked sidewalks, restaurant owners made their displeasure known, protesting at City Hall and filing a lawsuit.

In another era, their pressure campaign might have worked. For decades, the city’s mayors were Boston natives, men of Italian or Irish descent who were tight with local business owners and powerful unions.

Ms. Wu, 38, is different: a daughter of Taiwanese immigrants who campaigned as a catalyst for change and became the first woman and person of color ever elected to lead the city. She made a few minor concessions to the restaurants and moved on — but not before threatening to end outdoor dining altogether if they found her compromise unacceptable.

The clash revealed two things. True to her workhorse reputation, Ms. Wu is trying to avoid distractions as she hammers away at her campaign agenda, focused on “racial, economic and climate justice.” And true to Boston’s reputation, some old-school power brokers are pushing back against their loss of influence.

A coalition of property owners and brokers, the Greater Boston Real Estate Board, is prepared to spend $400,000 to squash Ms. Wu’s rent control plan, recently approved by the City Council. And the city’s primary police union, the Boston Police Patrolmen’s Association, has so far deflected her proposals, which include making it easier to fire officers for misconduct.

Union leaders say contract talks have reached an impasse, and they are seeking a move to arbitration, which in the past has resulted in favorable outcomes for the police.

Since Ms. Wu won election in 2021, her ambitious agenda endorsed by a sweeping 64 percent of voters, progressive leaders around the country have faced increasing scrutiny, in particular because of rising crime rates and homelessness.

Yet Boston remains its own ecosystem, and Ms. Wu still appears to have some running room. As the pandemic has ebbed, allowing her to focus more on her campaign priorities, some longtime political observers say the deepening resistance to her plans simply indicates that she is making headway.

Ms. Wu, who grew up in Chicago and moved to Boston in 2009 to attend Harvard Law School, has promised innovative approaches to climate change and a greener city, real advances on affordable housing, and long-sought checks and balances for the Police Department.

Her groundbreaking election, along with that of several new members on the Boston City Council — younger, more liberal and more racially diverse than their predecessors — signaled major shifts in the city of 650,000, where fewer than half the residents are white. The appetite for change has not diminished in the 18 months since then, said one of the new councilors, Kendra Lara.

“The cultural shift is salient; you can feel it,” said Ms. Lara, 33, a socialist who previously worked at the Boston-based social justice foundation Resist.

At the same time, the emergence of more diverse leadership has spurred ugliness, as well as more discussion of race and racism.

During her first weeks in office, Ms. Wu was the target of racist and sexist vitriol from across the country after she adopted aggressive measures to fight a resurgence of Covid-19, including a vaccine mandate for city workers.

Local critics of the mandate descended on the mayor’s home, staging noisy, early-morning protests that went on for months in 2022. The City Council president, Ed Flynn — whose father, Raymond Flynn, served as Boston’s mayor from 1984 to 1993 — voiced concern at the time about the “personal, vindictive” tone taken by some protesters.

“The demonstration under the white mayors was professional, it was respectful,” Mr. Flynn said at a meeting last year where a divided Council voted to prohibit residential demonstrations before 9 a.m.

This spring, Ms. Wu further restricted outdoor dining in the North End, barring it from streets and most sidewalks. In response, a handful of neighborhood restaurant owners returned to court with a new claim, now alleging that the mayor was discriminating against them because they were white men of Italian descent.

As evidence, they cited a joke she made at last year’s St. Patrick’s Day breakfast, an annual Boston tradition where politicians trade good-natured barbs. Ms. Wu quipped at the event that she was getting used to dealing with “problems that are expensive, disruptive and white. I’m talking about snowflakes — I mean snowstorms.”

One of the restaurant owners who sued her for discrimination, Christian Silvestri, said he could see no other explanation besides bias for the mayor to cripple his business, while allowing restaurants in the adjacent West End neighborhood to have tables on the street.

“The taxes we pay to the city are astronomical; we keep the city going,” he said. “She should be going to businesses, developers, labs, hotels, asking them, ‘As mayor, what can I do to help you grow?’ But that’s not happening — she has her own agenda.”

In an interview, Ms. Wu said her decision to curtail outdoor dining in the densely populated North End had been guided by pleas from residents, who had begged the city for relief.

“The people are our compass — what is important to people living in the city, who are trying their hardest to make life livable and fulfilling,” she said.

Her attention to quality of life and working-class concerns has shored up her support in some quarters. On Blue Hill Avenue in Roxbury, a woman trying to corral a stray dog outside a gas station said she liked what Ms. Wu had done to improve access to public transportation, eliminating fares on three city bus lines in low-income areas for a two-year trial.

Nemiah Brown, 60, a barber and part-time construction worker wearing a hard hat as he ate lunch outside in Dorchester, said he voted for Ms. Wu because she seemed focused on regular people. Told that the City Council had endorsed her plan for rent control, Mr. Brown nodded approvingly.

“I might be working over there,” he said, gesturing at a construction project rising above Morrissey Boulevard, in a fast-changing corner of the city, “but I can’t afford to live there.”

A recent poll found that 65 percent of Boston voters supported rent control, as the median rent for a one-bedroom apartment in the city hovered around $3,000 per month. But Ms. Wu’s proposal, which would limit annual rent hikes to between 6 and 10 percent, depending on inflation, still faces steep hurdles.

It must be approved by the state legislature and the governor, and Greg Vasil, the chief executive of the Greater Boston Real Estate Board, said the group will continue to fight it, convinced that it will do more long-term harm than good by driving developers away from the city.

Frequently typecast as a “big ideas” mayor, less interested in daily grit, Ms. Wu has recently announced a series of smaller, quicker innovations that could be seen as the millennial version of pothole repair: new bike lanes; a curbside composting program; a beer garden in Boston Common; and more dog-friendly restaurant options.

Such changes do not impress Jim Napolitano, 68, and other longtime East Boston residents who were holding court in the back of a neighborhood market on Wednesday morning, as Ms. Wu held a community coffee hour at a playground a few blocks away.

“The yuppies might like it, but we’re all set on bike lanes,” Mr. Napolitano said. “We’d like her to fix the streets.”

In East Boston, as in the city’s other old Irish and Italian American power centers, Mr. Napolitano and others said they felt forgotten by a mayor who seemed intent on nudging the city forward without them.

“We want her to know that there are other people in the city besides poor people and people of color,” he said. “You still have the base, the Italian people. You have conservatives, which she doesn’t realize.”

The police, too, have dug in their heels against Ms. Wu’s proposals. The mayor sent a strong message last summer by appointing a new police commissioner, Michael A. Cox Sr., who was himself a victim of misconduct by his fellow Boston officers 30 years ago. But bending the terms of the police contract will be exceedingly difficult.

“With an institution as entrenched as this Police Department, as set in its ways, you need a dragon slayer,” said Jamarhl Crawford, a community activist who served on the city’s Police Reform Task Force in 2020.

Crime has not surged in Boston as it has in other places, though there have been 17 murders in the city this year, compared with 10 in the same period in 2022. The rate remains among the lowest in decades, and the incidence of most other types of crimes has fallen or remained stable, making the issue less of a preoccupation for Ms. Wu than it has been for other big-city mayors in the pandemic’s wake.

She takes a measured tone in her public comments about policing, emphasizing officers’ morale and the difficulty of their work. That approach, along with her proposal for a modest increase to the police budget next year, has not been lost on the union, which saves its harshest criticism for the City Council. But Ms. Wu has also made it clear that there will be no contract deal without the changes she views as crucial, even if the police contract ends up in arbitration.

Greeting residents at the well-attended coffee hour in East Boston, bundled up in a hooded sweatshirt bearing the name of a neighborhood soup kitchen, Ms. Wu listened intently as one after another lined up to voice concerns.

Mary Berninger, a resident for decades, told Ms. Wu she was frustrated with continuing development and the loss of parking. She came away unsatisfied.

The mayor “has a heart of gold,” Ms. Berninger said. “But she’s surrounded herself with people who can’t recognize that there is an established community in Boston that needs to be heard.”