Presidential contender Pete Buttigieg responded Friday to Sen. Elizabeth Warren’s criticism of his high-dollar fundraisers, saying that if “doing traditional fundraisers disqualifies you from running for president, I guess neither one of us would be here.”

In an interview as part of The Washington Post Live’s candidate series, Buttigieg added, “The thing about these purity tests is the people issuing them can’t even meet them.”

Warren held closed-door fundraisers during her 2018 Senate race before eschewing them in her run for president. For weeks, Warren and Buttigieg have been exchanging barbs as Warren questions Buttigieg’s time at a business consulting firm and he takes aim at her work providing legal advice to companies.

Warren also has been urging Buttigieg, the mayor of South Bend, Ind., to open his fundraisers to the media and disclose the names of those raising money for him, which he has agreed to do. Liberal activists have taken to dogging his events with signs calling him names like “Wall Street Pete.”

“It is a little strange, because I think that I broadly share the same values and hopes as a lot of these folks,” Buttigieg said. “It’s a little hard to have a conversation with them, so I don’t know for sure.”

He added, “Part of our democratic process, and all of its messy beauty, is that individuals can choose whether they’re going to focus on supporting a candidate that they believe in, or coming to something you’re doing and holding up the sign or chanting. That’s fine. It’s democracy.”

Warren has also signaled a weariness with their recent back-and-forth recently, saying in a speech Thursday, “Nobody is perfect, and nobody is pure.”

In a wide-ranging 40-minute interview, The Post’s Robert Costa pressed Buttigieg on the criticism leveled at his work for the consulting giant McKinsey & Co. Earlier this week, Buttigieg’s campaign released the names of the clients he helped at McKinsey, including Blue Cross Blue Shield of Michigan.

Costa asked Buttigieg if anything about his work there gave him pause.

“Well, it certainly made me aware of how big an insurance company can get, and how governments aren’t the only things that can get bureaucratic,” the mayor said. “I learned enough to get a sense of why doing something in the private sector isn’t automatically better than the public sector.”

But he said he had no regrets about working for McKinsey.

Costa also asked Buttigieg about his electability, including his ability to appeal to minority voters and what he has learned from spending time in minority communities on the campaign trail.

Buttigieg argued that his own party could do a better job keeping its promises, citing “the extent to which there are a lot of African American voters who feel totally abused by the Republican Party — but sometimes taken for granted by Democrats.” He said he had recently visited a town in South Carolina that had not seen a presidential candidate for a decade.

More broadly, the mayor took aim at what he described as a belief that candidates can address either white rural voters or black urban ones, but not both. He challenged “the assumption that, for example, we can either reach out to rural America, which people imagine in a very white way, or we can focus on issues of racial justice.” In much of the South, as in other places, he said, rural issues and racial justice often coincide.

Racial issues have figured prominently in Buttigieg’s challenges, as he has struggled to attract diverse crowds and minority support, while facing criticism from African American activists in his hometown of South Bend.

Costa cited a study by the group Democracy in Color showing that only a small percentage of South Bend’s government contracts went to minority businesses during Buttigieg’s tenure. Buttigieg responded that he was the one who sought a study of those disparities in the first place, and that creating and implementing new targets takes time.

“Of course we haven’t solved or ended these inequities or issues in our city, or in any place in America,” Buttigieg said. “What I’ll say is I have acted with commitment.”

Buttigieg declined to commit to choosing a person of color as his vice president — suggesting it would be premature to set forth any requirements for the position — but he pledged to make his Cabinet racially diverse and ensure that at least half the Cabinet would be women.

More personally, Buttigieg took on his own identity, saying he thinks America is “absolutely” ready for an openly gay president. The 37-year-old is the most prominent openly gay figure to seek the presidency, and his husband, Chasten, has become a high-profile part of his campaign.

With Democrats desperate to defeat President Trump, much of the discussion in the primary has surrounded electability. Buttigieg said Democrats tend to “overthink” such issues, arguing that every recent Democratic president has been — like him — new to the national stage, an aspirational figure who represents a new generation.

He dismissed the notion that Democrats would lose voters they need if they nominate an openly gay candidate.

“Look, if you’re a single-issue voter, and your single issue is about being anti-LGBT, then you’re probably not one of the voters available to us,” Buttigieg said.