In a city known for its unions, two loom over the Paul Vallas-Brandon Johnson race, and no labor leader is as significant as the incendiary president of the Fraternal Order of Police.CHICAGO — When Bobby L. Rush, the Black Panther turned congressman turned elder statesman of this city’s South Side, stood last week to endorse Paul Vallas for mayor, the first question he confronted featured his own words.How could a man who just two and a half years ago called Chicago’s Fraternal Order of Police “the most rabid, racist body of criminal lawlessness by police in the land” stand behind Mr. Vallas, the candidate endorsed by that police union?“I have no patience for their leadership,” whom “I detest,” Mr. Rush said, thronged by supporters with Mr. Vallas by his side. But, he added, “I had my son killed by street violence. I cannot be antipolice.”In a city where organized labor remains a powerful symbolic and organizational force, two unions have loomed over the race for Chicago mayor, which ends with a fiercely contested runoff election on April 4: Chicago’s Lodge 7 of the Fraternal Order of Police, which backs the more conservative Democrat in the race, Mr. Vallas, and the Chicago Teachers Union, which backs the Cook County commissioner Brandon Johnson, a C.T.U. member and former teacher.Both unions offer considerable muscle, which could prove vital if turnout remains around the 36 percent who came out for the first round of voting on Feb. 28. The teachers union has put $1.2 million behind Mr. Johnson, with a further $1 million coming from the national and Illinois federations of teachers. Armies of door knockers and phone bankers are pitching in, while the police union presses its members to volunteer for the final Vallas sprint.But no other union in the nation’s third-largest city carries the same liabilities either. An 11-day teachers strike near the beginning of the 2019 school year pitted the educators’ union against City Hall and many parents. Then schools shut again last year with the teachers union again at loggerheads with the city, this time over coronavirus policies as parents prepared to send their children back to in-person instruction.John Catanzara, president of Chicago’s Lodge 7 of the Fraternal Order of Police, which has backed Mr. Vallas. Mr. Johnson’s campaign has tried to tie Mr. Vallas’s tough-on-crime talk to the incendiary views of Mr. Catanzara.Ashlee Rezin/Chicago Sun-Times, via Associated PressStill, there is nothing quite like Chicago’s relationship with the Fraternal Order of Police, especially with its president, John Catanzara, who expressed sympathies for the rioters who stormed the Capitol on Jan. 6, 2021, called Muslims “savages” who “all deserve a bullet” and retired from the police force in 2021 rather than face potential disciplinary actions. He punctuated his retirement papers with a handwritten note, “Finally!!! Let’s go Brandon,” a stand-in phrase for a more vulgar insult against President Biden.“When they talk about the F.O.P., they’re talking about me, which is hilarious,” Mr. Catanzara said in an interview, conceding, “If I got paid a dollar every time I was called a racist, I’d be an independently wealthy man.”In a mayoral campaign that has revolved around the two candidates’ very different stances on policing and public safety, Mr. Johnson’s campaign has tried to tie Mr. Vallas’s tough-on-crime talk to the incendiary views of Mr. Catanzara. One recent flier aimed at Latino neighborhoods compared Mr. Johnson’s promises — “Brandon will train and promote 200 new detectives” — to a single aspect of Mr. Vallas’s public safety record: “Vallas is endorsed by the Fraternal Order of Police.”Mr. Catanzara’s Facebook post about Muslims has been a talking point in the multicultural quarters of this racially, ethnically and religiously diverse metropolis. And Johnson campaign workers are quick to link Mr. Vallas to the extended comments that Mr. Catanzara made to a Chicago public radio reporter about the Capitol rioters, which included, “There was no arson, there was no burning of anything, there was no looting, there was very little destruction of property. It was a bunch of pissed-off people that feel an election was stolen, somehow, some way.”Mr. Rush’s endorsement of Mr. Vallas, a potential boost for the white candidate facing skepticism among some Black voters, elicited reminders from the Johnson campaign of an interview in Politico where Mr. Rush said the police union “stands shoulder to shoulder with the Ku Klux Klan.”The broader aim is to convince Chicagoans that Mr. Vallas is some kind of secret Republican in a city dominated by Democrats. Linking him with Mr. Catanzara, an outspoken supporter of former President Donald J. Trump, is a key to that strategy, Johnson campaign aides said. Mr. Johnson did not have to name names during a debate last Tuesday night when he accused his opponent of hanging out with people in the “extreme Republican Party who did not believe the pandemic was real.” (Mr. Catanzara urged police officers in 2021 to defy the city’s vaccine mandate.)Paul Vallas speaks to supporters after advancing to the April runoff last month.Taylor Glascock for The New York TimesLittle wonder that Mr. Rush, who retired from the House last year, spent his initial comments on Tuesday vouching for Mr. Vallas as “a lifelong Democrat” and a “South Side Democrat” who “ain’t nothing but a Democrat.”In Chicago, unions stretch well beyond teachers and police, and organized labor — facing two starkly different candidates in a contest that has already sunk the incumbent mayor, Lori Lightfoot — is as divided as the city itself. Local 150 of the International Union of Operating Engineers has backed Mr. Vallas after its preferred candidate, Representative Jesús G. García, failed to make the runoff. So have union locals representing firefighters, ironworkers, elevator constructors, plumbers and electricians.Beyond the teachers unions, Mr. Johnson’s union backers include service workers, nurses and government employees.But Mr. Catanzara is a presence like none other, so much so that Mr. Vallas has made a show of not taking money from the Fraternal Order of Police or accepting any formal organizing muscle. When Ja’Mal Green, a 27-year-old activist who tried and failed to make the mayoral runoff, surprised the city by endorsing Mr. Vallas, he made a point of posting a video pressing his chosen candidate to say he is not beholden to the police union.“I’m not beholden to anybody,” Mr. Vallas responded.Mr. Catanzara is not lying low. He predicted that 800 to 1,000 Chicago police officers would leave the force if Mr. Johnson wins, adding to hundreds of vacancies already awaiting the next mayor.“If this guy gets in we’re going to see an exodus like we’ve never seen before,” he said, predicting “blood in the streets.”Mr. Catanzara was particularly hard on the teachers union and its “Manchurian candidate.”“They’re definitely pushing all their chips into the pot here,” he said.As for those who cast him as a bigoted bomb thrower, Mr. Catanzara just waved his hands. “I don’t waste my breath with them,” he said. “Like I tell everyone, read the book, not the cover.”Brandon Johnson, the Cook County commissioner, is a former teacher and member of the Chicago Teachers Union, which has endorsed him.Jim Vondruska for The New York TimesHis presence is especially troubling for Black Chicagoans, who must balance their concern over violent crime against their troubles with a police department that has been laboring under a federal consent decree after the Justice Department found routine use of excessive force. Mr. Johnson is Black. Mr. Vallas is white. And race has been a dividing line in Chicago politics since the city elected its first Black mayor, Harold Washington, in 1983.Last week, Paris Walker and her sister Emma gathered with others in Chicago’s historic Bronzeville neighborhood to march with Mr. Vallas and Mr. Rush to the storefront Beloved Community Church of God in Christ, where the former congressman was to bestow his blessing. Paris Walker shrugged off Mr. Vallas’s ties to the police union and said Mr. Johnson lacked the experience to run a city of Chicago’s size and complexity.Emma Walker was not as sure as she recounted menacing traffic stops, unwarranted violence and general intimidation from the Chicago police.“It bothers me,” she said of Mr. Vallas’s police union ties. “The police need a lot of cleaning up.” More