PHOENIX — They packed into the room to cheer their heroes.

The crowd of more than 100 hollered enthusiastically at Mr Henry Cejudo, a local hero and Olympic gold medallist, the son of undocumented immigrants from Mexico who had gone on to become a mixed martial arts superstar.

But they were really there to celebrate US President Donald Trump.

Wearing red Make America Great Again hats, several men held giant American flags and stood in front of several campaign signs: “Latinos for Trump”, “Cops for Trump” and another imploring them to text “Woke” to get the latest information on the campaign.

In the words of Mr Eric Trump, the president’s son and the headliner of the event, the battle is simple. It’s right versus wrong, he said, to a loud round of cheers.

“They are trying to cancel our voice, guys.”

Men are the core of Mr Trump’s base. In polling, gender gaps exist in nearly every demographic: among white voters, among senior citizens, among voters without a college degree, men are far more likely than women to support his reelection. And little of that support has shifted in the days since Mr Trump announced he had tested positive for the coronavirus. Polls suggest that this presidential election could result in the largest gender gap since the passage of the 19th Amendment a century ago.

Then there is one of the most enduring questions of the Trump appeal: Who are the nearly 30 per cent of Hispanic voters who say they support him, despite his anti-immigration rhetoric and policies?

There is no one simple answer. Mr Trump has strong backing from Cuban and Venezuelan exiles in South Florida, who like his stance against communism. And his campaign has heavily courted evangelical Latinos throughout the country. But no other group worries Democrats more than American-born Hispanic men, particularly those under the age 45, who polls show are highly sceptical of former vice-president Joe Biden.

Yet what has alienated so many older, female and suburban voters is a key part of Mr Trump’s appeal to these men, interviews with dozens of Mexican-American men supporting Mr Trump shows: To them, the macho allure of Mr Trump is undeniable. He is forceful, wealthy and, most important, unapologetic. In a world where at any moment someone might be attacked for saying the wrong thing, he says the wrong thing all the time and does not bother with self-flagellation.

“I feel so powerful,” the president declared at a rally in Florida on Oct 12, standing in front of Air Force One. Lest anyone miss the message, the rally ended with “Macho Man” by the Village People blasting on the speakers.

Mr Paul Ollarsaba Jr, a 41-year-old Marine veteran, voted for a Republican for the first time in 2016, won over by what he saw as Mr Trump’s commitment to the military.

“I am Mexican,” Mr Ollarsaba said, adding that for years he thought that meant he had to vote for Democrats. When he began supporting Mr Trump in 2016, his family ostracised him. “My parents say: ‘Why are you supporting a racist? You’re Mexican, you have to vote this way,’” he said. “No, it’s my country. It’s fear, people are afraid of saying they support the president.”

Mr Cejudo clearly had no such fear. When Mr Trump hosted large rallies in Nevada last month, Mr Cejudo joined several other MMA fighters who backed his campaign.

“I’ve been the biggest fan of him,” said Mr Cejudo, 33, recalling watching “The Apprentice” in a high school class. “We need a businessman, we need somebody like this to run our country.”

Other attendees at the event with Mr Cejudo and Mr Eric Trump spoke of watching Mr Trump on “The Apprentice”, saying they liked his strong style, his apparent confidence in his own opinions. In interviews, they said they viewed his actions as president much in the same way: Even those they do not wholeheartedly agree with, they see as further evidence of his strength.

They said they saw his defiance of widely accepted medical guidance in the face of his own illness not as a sign of poor leadership, but one of a man who does his own research to reach his own conclusion. They see his disdain for masks as an example of his toughness, his incessant interruptions during the debate with Mr Biden as an effective use of his power.

“We saw him being a boss,” said Mr Edwin Gonzales, 31, who held a large American flag outside the Trump campaign office. “And for him to go down the escalator is basically the same thing — it’s like, ‘Dang, the boss has stepped down and he’s putting himself out there to be the president.’ That’s what’s exciting.”

Mr Gonzales added that for him, and many other Trump supporters, the president represented the best of capitalism, adding, “He’s a boss and they wanted to be him, they idolise him.”

At the event, voters said they admired Mr Trump and also criticised Mr Biden, whom many of these supporters described as weak and deserving of the derogatory label coined by the Trump campaign: “Basement Biden”.

Indeed, many of these men dismiss the need for masks themselves. After being screened with temperature checks at the event with Mr Eric Trump and Mr Cejudo, almost none of the audience members wore a mask, nor did any of the speakers.

Mr Biden has mocked Mr Trump’s reluctance over masks. “What is this macho thing, ‘I’m not going to wear a mask’?” he said during one town hall event this month. The comment prompted a commentator on Fox to retort that Mr Biden “might as well carry a purse with that mask”.

“We’re at a turning point in this country where we can either be afraid or move forward,” said Mr Ricco Rossi, 40. “I think what they have done in the last few months, they have damaged their party more. They try to scare us.”

Though Hispanic women overwhelmingly support Mr Biden, Hispanic men appear to have a persistent discomfort, with polls showing him struggling to maintain more than 60 per cent of the group, far below his average among nonwhite voters. (Polls show him still well ahead of Mr Trump’s roughly 30 per cent support from Hispanic voters.) Mr Biden has not done enough to directly reach out to these young Latino men, Republican and Democratic strategists say.

“You have these US-born Hispanic males under 40 who are pretty Trumpy, the question is why?” said Mr Mike Madrid, a Republican consultant involved with the Lincoln Project, which is working to get Mr Trump out of the White House.

Both parties have often focused their outreach efforts on white, working-class voters, though many Hispanic men share the same basic priorities. “They’re English dominant, they are facing very similar economic situations, listening to the same media,” Mr Madrid said.

After facing months of persistent criticism that it was not doing enough to reach out to Latino voters, the Biden campaign has released several Spanish language advertisements in the last few weeks, including one featuring Bad Bunny, a pop star known for his gender-fluid style. Other advertisements focus heavily on the way the Trump administration has targeted Latinos, a message that simply does not resonate among men who do not want to see themselves pitied.

Some Democrats argue that the support for Mr Trump is an example of machismo culture, venerating traditional gender roles and a kind of hyper-masculinity. But the enthusiasm hints at some of the underlying trends among US-born Latinos. More Hispanic women than men attend and graduate from college, while Hispanic men tend to be overrepresented in law enforcement institutions, including the military, the Border Patrol and Immigration and Customs Enforcement.

Yet the admiration of Mr Trump reveals something deeper as well. Democratic pollsters who have closely tracked Hispanic men say they are more likely to prioritise jobs and the economy and less likely to be concerned about immigration and racism. Many Hispanic men are singularly focused on earning a living, gaining an economic edge that they can pass on to their children. There is a deep belief in an up-by-your-bootstraps mentality — and that Mr Trump did no such thing seems utterly beside the point.

Mr Joshua Tapia, a 35-year-old cashier, said that before the pandemic, he believed he was much better off economically, because he started investing in the stock market. And now?

“A lot of jobs are suffering right now, and I don’t blame Trump, I just blame circumstances, unfortunately,” he said. “Nobody could have seen how this played out.”

Even devoted Democrats have criticised Mr Biden for offering a somewhat fuzzy economic message, at a time when the pandemic has left more than 10 per cent of Latinos unemployed and many more with a reduction in wages.

“In the Latino community, you are defined by your ability to provide,” said Mr Tomas Robles Jr, an executive director of Lucha, a progressive group that is campaigning for Mr Biden and other Democrats in Arizona. “Folks who live in a perpetual state of economic insecurity want to look around and at least believe that you can do great in this economy. Biden needs to have a message that they matter, that he is going to create an economic reality they have the ability to make it.”

In interviews with scores of Hispanic Trump supporters at events in Florida, New Mexico, Nevada and Arizona over the last year, nearly everyone said their politics angered some friends and family, and rejected any suggestion that their support was based on anti-immigrant attitudes.

And it is not quite assimilation either: These men are proud to be Latino, children and grandchildren of Mexican immigrants specifically, and many have made an effort to continue speaking Spanish.

Many say there is some appeal in being a political curiosity and voting differently than the vast majority of Latinos.

Even Mr Cejudo, the MMA star, told the enthusiastic crowd in South Phoenix that he had been shunned for his views, which had made him only more outspoken.

“Getting backlash as a Latino, you know what that tells me,” he said. “That there’s a lot of ignorance in this game.”

He told the group — supporters of a president whose first campaign was largely built on opposing illegal immigration — that his own mother came from Mexico “in a politically incorrect way”. He said his father was later deported, while his mother helped him nurture his dreams of becoming an Olympian.

Then he posed for pictures with a flashy bicep flex. THE NEW YORK TIMES