Over the course of two decades, the New York City Republican Party got two mayors elected in deep blue New York City. It was a neat trick made possible by the party’s ability to toe a centrist line — conservative on the budget, liberal on social issues.

But that line has shifted in the era of President Trump, and so has the idea of a New York City Republican.

The Metropolitan Republican Club in Manhattan, whose members have included Theodore Roosevelt and Nelson A. Rockefeller, has in the last two years hosted talks by Steve Bannon; the Breitbart News editor, Joel Pollak; and the Proud Boys founder, Gavin McInnes.

Republicans are now outnumbered by Democrats in Manhattan by nearly eight to one, and some prominent New Yorkers like Joseph Lhota, the 2013 Republican candidate for mayor, have left the party.

“It had to do with Donald Trump, as head of the party,” Mr. Lhota said. “I just couldn’t deal with it.”

Few things embody the change more than the Manhattan Republican Party, and the divergent paths of the city’s two former Republican mayors from Manhattan: Michael R. Bloomberg, who is now a Democrat, and Rudolph W. Giuliani.

In a vitriolic speech in New York in September, Mr. Giuliani said that Mayor Bill de Blasio’s biracial son should fear “another Black” more than a police officer, and that Black Lives Matter protesters are “cop killers” who might also want to kill white people.

“When you see a police officer killed, which you are watching, somebody is carrying out what Black Lives Matter asked them to do,” Mr. Giuliani said. “Or if you see a white person killed, it could be that, too.”

Mr. Giuliani made his remarks at a forum hosted by the Manhattan Republican Party, which is now run by the family of John Catsimatidis, a billionaire Republican grocery magnate who has run for mayor. He has given the majority of the party’s recent political donations; his daughter, Andrea, 30, is the party chair.

Mr. Catsimatidis has evolved from a self-described undecided voter at the 2016 Republican convention to a full-throated Trump supporter in 2020.

“If you vote on personality, Trump loses. If you vote on performance, Trump wins,” Mr. Catsimatidis said.

Ms. Catsimatidis also wholly embraces Trumpism, including the president’s rhetoric about New York City, and saw Mr. Giuliani’s recent speech as a way to highlight the city’s perils in the time of Covid: the frustrated small business owners, the cuts to sanitation services, the rise in shootings.

The event “was our way of becoming more conspicuous,” she said.

The party’s politics have veered so far in the direction of Mr. Trump that they have become virtually unrecognizable to moderate Republicans of years past.

In interview after interview, formerly active Manhattan Republicans said their disaffection with the president prompted them to leave the party or withdraw from local activities. Several are now openly campaigning for former Vice President Joseph R. Biden Jr.

“It’s been very sad to see what’s happened,” said John Ravitz, who chaired the Manhattan Republican Party in 2001 and 2002.

The party has a handful of elected officials in New York City, with most from Staten Island, including James S. Oddo, the borough president, and Nicole Malliotakis, a state assemblywoman who is trying to unseat Representative Max Rose in a congressional district that includes Staten Island and Bay Ridge, Brooklyn.

She distanced herself from the president during her 2017 run for mayor, but now embraces him, boasting of Mr. Trump’s “complete and total endorsement” in her race against Mr. Rose.

There are no Republicans from Manhattan in Congress, the City Council or the State Legislature.

The Republicans are thought to have just one potentially viable candidate this election in Manhattan: Lou Puliafito, a doorman who is running for Assembly in a district where the incumbent was thrown off the Democratic and Working Families Party ballot lines for filing her paperwork incorrectly.

Among the party’s 11 long-shot candidates is Mike Zumbluskas, an Independence Party member whom the Manhattan Republicans cross-endorsed for State Senate.

He supports Mr. Trump’s embrace of hydroxychloroquine as a treatment for coronavirus — which the president tested positive for early this month — despite a lack of scientific evidence that it’s effective; argues New York’s lockdown has been too onerous; and says the president’s management of the pandemic has garnered undue criticism.

“If you look what he was doing behind the scenes, he was taking it seriously,” Mr. Zumbluskas said. “He was making calls.”

Not that Mr. Zumbluskas’s views necessarily matter, from an electoral perspective.

“The candidates are almost beside the point in a place like Manhattan, because they’re not viable up and down the ballot,” said Neal Kwatra, a New York City Democratic strategist.

Rather, Mr. Kwatra said, the party has the potential to become a “fund-raising vehicle” or vanity project for party building, donor cultivation and political organizing for the Catsimatidis family writ large.

As of February, there were 109,269 voters registered in the Republican Party in Manhattan, compared to 832,312 registered Democrats. That’s a nearly 8-to-1 ratio, versus the 6-to-1 ratio at the time Mr. Giuliani was elected.

“With a few exceptions, they’re not putting up credible people,” said Stu Loeser, a longtime adviser to Mr. Bloomberg. “Just being the party of, ‘We support the cops no matter what,’ and ‘the other party supposedly opposes the cops no matter what,’ that’s not really a governing philosophy. That’s a tactic.”

Funding for the Republican Party in Manhattan has also tapered off in recent years. Of the two accounts controlled directly by the New York Republican County Committee, one has a $1,500 debt, according to its filing in July; the other has nearly $18,000. That second account, meant for housekeeping and party building purposes, raised nearly $52,000 from individuals between February and July from just 16 donations. Nearly all of it —  $50,000 — came in two donations, both from Mr. Catsimatidis.

Ms. Catsimatidis, the Manhattan party chair, said that it is possible to support Mr. Trump while being a moderate. A supporter need not embrace all of his positions in the way she does, she contended.

But that opinion appears to be largely held by Trump Republicans. Andrew Sidamon-Eristoff, a former councilman from Manhattan’s East Side and a Biden Republican, said the party has become woefully out of touch with centrists in New York City.

“If you’re not even part of the conversation, the tendency is to start talking to yourself and to become inexorably more strident and more resistant to alternative ways of thinking, less empathetic,” he said.

At the recent Manhattan G.O.P. event featuring Mr. Giuliani, Mr. Catsimatidis, who has said he may run for mayor again, referred to the homeless men living at an Upper West Side hotel as “criminals.”

Curtis Sliwa, the founder of the Guardian Angels and a declared mayoral candidate, said at the event that if he was elected, he would push for the criminal prosecution of Mr. de Blasio and his wife, Chirlane McCray.

But the star of the show was Mr. Giuliani, now an adviser to the president who uses words like “invasion” and “killers” to describe newcomers to the United States.

In recent days, Mr. Giuliani has garnered attention for giving The New York Post an electronic copy of an email that purportedly showed that Joseph R. Biden Jr. had met with an adviser to a Ukrainian energy company on whose board Hunter Biden served. The authenticity of the correspondence could not be verified, and the incident seemed to weaken the credibility of Mr. Giuliani, who has been accused this election cycle of taking information from Russian agents.

But in the speech in September, Mr. Giuliani was in usual form, tearing into the mayoralty of Mr. de Blasio and regaling the audience with tales of his own mayoral successes.

Mr. de Blasio, he said, is “the worst mayor in the history of New York City.”

The conditions of schools under the current mayor is a “sin,” and his schools chancellor, Richard A. Carranza, “belongs in Cuba,” Mr. Giuliani said.

Mr. Carranza was born in Arizona and is of Mexican descent.

Moderate Republicans argue that this sort of rhetoric just drives voters away.

“I keep hoping that the discipline of losing elections will maybe prompt people to begin rethinking their approach,” Mr. Sidamon-Eristoff said.“If you’re constantly losing elections, maybe it’s time to look inward and ask yourself why.”