It was the kind of welcome of which some presidential candidates, campaigning for months, might have been jealous.

Well before the former Texas congressman Beto O’Rourke arrived wearing a green Plymouth State University baseball cap, students and local Democrats had filled the large atrium where he was due to speak.

The town hall event was on a Wednesday morning, a time when students have classes and other people have work, potentially a recipe for sparse audiences here in the lightly populated foothills of New Hampshire’s White Mountains.

But O’Rourke draws crowds and cameras wherever he goes, despite his campaign being young, despite a lack of detailed policies and despite his having skipped the flirtatious trips to New Hampshire that are considered customary before a candidacy is announced.

The field of Democratic candidates for the 2020 presidential nomination is the most diverse ever, filled with women, candidates from minority backgrounds and one openly gay man. The party’s base is diverse too, with four of 10 Democratic voters anticipated to be non-white. In 2008 and 2016, the party put forward a black nominee and a woman.

But three of the top-polling candidates for 2020 so far are white men: Vermont senator Bernie Sanders, O’Rourke and former vice-president Joe Biden, who has not even declared his candidacy. Does that present a problem?

In New Hampshire in recent days, Democratic voters who spoke to the Guardian laid out a simple answer. Yes, it would be nice to have a woman or a minority candidate but the focus must remain on removing Donald Trump from office. Whether the most electable candidate will be a woman or a member of a minority remains to be seen, but undecided voters are willing to consider a white man if he is determined to have the best shot at the White House.

“I think Democrats, myself included, are willing to wait for that [for a woman nominee] in order to simply win, to get Trump out of office,” said Marilee Lin, 54, a prep school teacher who watched O’Rourke speak in Plymouth. “At this point it’s kind of a pragmatic election. We’ll regress even further if we can’t win.”

The first primaries are many months away and nothing is set in stone. Political scientists warn that poll numbers are tied almost solely to name recognition. At this point in the 2016 primary, Sanders was polling in the single digits against Hillary Clinton. Ultimately, he ran her close. Trump entered the Republican field in June 2015. He also started off with very low poll numbers.

What is certain is that the diversity of the Democratic field is making race, gender and sexuality – as well as the privilege associated with each – things white male candidates have no option but to talk about.

“No candidate can make it to 1600 Pennsylvania Avenue and not talk about race,” said Rashad Robinson, executive director of the racial justice organization Color of Change.

“The Democratic nominee and perhaps the next president will have to demonstrate proficiency in bridging cultural divides so that electoral coalitions may be assembled across them,” said Michael Cornfield, a professor of political management at George Washington University.

Bernie Sanders is entering the race as a frontrunner this time around. Photograph: Richard Vogel/AP

O’Rourke has said it is “undeniable” he has benefitted from white privilege. In his stump speeches he is quick to get to racial and gender inequalities and the need to address them.

For some, though, he has become the poster child of white male privilege. He went to boarding school, then an Ivy League college. He was arrested twice, the second time for driving under the influence, but it does not seem to have derailed him as it might others. After he failed to beat Ted Cruz in a Senate race last year, he traveled across the country, publicly mulling whether he should run for president. When he decided he would, he told Vanity Fair he was “just born to be in it”.

“It’s impossible to imagine a female candidate for whom this approach could work,” wrote Danielle Tcholakian in the Daily Beast. “Can you imagine if Stacey Abrams went on a vision-quest road trip, joked that her spouse (who happens to be the primary breadwinner in the family) mostly raises her kids, then rambled at a camera for three and a half minutes to announce she is simply called to be president?”

Earlier this week, the New York Times asked Andrew Gillum, a black Florida Democrat who lost a race for governor, why he or Stacey Abrams, a black woman who lost a race in Georgia, did not run for president.

“There’s no doubt that O’Rourke enjoys a set of privileges in his decision making that other candidates don’t,” said Gillum.

It’s not enough to sort of feel peoples’ pain. I’m not interested in a therapist Rashad Robinson, Color of Change

For Robinson, it’s not enough for straight white men to talk about their privilege: they need to understand it, he says, to show how they have confronted it and to display policies that will make the country more equitable.

“There’s nothing worse than someone explaining that they have privilege and then keep operating the same way they’ve always operated,” he said. “Voters more and more don’t want lip service, we don’t want you to stay on beat in our churches or tell us your favorite hip-hop album. We want you to be able to talk about what policies and what systemic changes you will make. It’s not enough to sort of feel peoples’ pain. I’m not interested in a therapist.”

The diversity of the field has also meant that men can expect to be asked if they will commit to appointing a female running mate, while there has been criticism of the apparent media fixation with the three white men at the front of the pack.

“I’m not disrespecting Beto but he’s getting a disproportionate amount of coverage,” said Pat Cantor, 60, a professor of early childhood studies at Plymouth State University. “I do think … that women candidates get a different kind of scrutiny and immediately the conversation goes to likability in a way it doesn’t with men.”

The website FiveThirtyEight, looking at coverage by CNN, Fox News and MSNBC, found that compared to other candidates, O’Rourke and Sanders saw “mountainous peaks in mentions” following their announcements.

Joe Biden waves after delivering remarks to the International Association of Fire Fighters Legislative Conference in Washington. Photograph: UPI/Barcroft Images

“There is no question that the media does not do an equal and fair job of covering women and minority candidates – that they ask them different questions, that they give them less attention and coverage,” said Matt Barreto, a professor of political science and Chicano studies at the University of California, Los Angeles and the co-founder of the polling firm Latino Decisions.

Barreto sees race potentially playing a major role in how minorities in the Democratic base choose to cast their ballots.

“If your group does not have parity in terms of elected office of your population size, those voters tend to want to see more candidates from their race and ethnicity in politics because they feel they can relate and understand their community better and will do a better job representing them,” he said.

However, he added that he thought “beating Trump is the number one issue that Democratic voters are mentioning in polling and focus groups. I would imagine that’s where all the energy is going to be.”

That appears to remain the focus of many voters in New Hampshire. Gaye Fedorchak, 64, saw O’Rourke speak at a coffee shop in Laconia on Thursday. The audience spilled on to the sidewalk and the fire marshal had to end the event early.

While Fedorchak said she was also interested in Harris, former San Antonio mayor Julian Cástro and South Bend, Indiana mayor Pete Buttigieg, she said winnability would ultimately outweigh diversity when she decided who to support.