Democratic 2020 presidential hopeful says change will occur when voters see his policies will work in their interests

Opposition to gay marriage among African Americans will “start to wash away”, Pete Buttigieg said on Sunday, when such voters “struggling to get on to right side of history” see he will work in their interests.

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The mayor of South Bend, Indiana, spoke to CNN’s State of the Union from Georgetown, South Carolina, a crucial early voting state which this weekend played host to a number of candidates for the Democratic presidential nomination.

Buttigieg, 37, is in the top five in most polls but has not built on an initial surge. A national Fox News poll released this week gave Joe Biden, the former vice-president, a familiar healthy lead among African American Democratic primary voters, over three senators: Bernie Sanders of Vermont, Kamala Harris of California and Elizabeth Warren from Massachusetts.

Polling also shows that less than half black Protestant Christians, a key voting bloc, support same-sex marriage. Buttigieg has also faced controversy arising from an officer-involved shooting of an African American man in South Bend in June but on CNN the candidate, who is married, was asked if being gay was part of what was holding him back with at least some black voters.

“I think most black voters like most voters in general want to know what the candidates are actually going to do to improve their lives,” he said. “And when I talk to black voters in particular there’s a sense of having been taken for granted in politics in the sense that candidates haven’t always been speaking to them in terms of gaining their trust.”

Mentioning policy proposals, Buttigieg cited his Douglass plan, named for the great 19th-century anti-slavery campaigner Frederick Douglass, that attempts to tackle “institutional racism that works on health”.

He continued: “I think that a lot of these other factors start to wash away once voters understand what it’s going to mean for them that you versus the others are running for office. But we’ve got six months to make sure we get that message out … and that’s how I plan to earn support among black voters whether it’s here or across the country.”

Buttigieg has been fiercely critical of Mike Pence. Like him, the vice-president is from Indiana, but an evangelical Christian and social conservative with an anti-LGBTQ record in office. On CNN, the mayor was asked if such criticism could also apply to African American primary voters who oppose gay marriage.

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“Well,” he said, “I think back to my experience in Indiana when I was running for re-election after I came out in a community that’s generally Democratic but also quite socially conservative. And I just laid out the case on the kind of job that I was doing.

“And what I found was that a lot of people were able to move past old prejudices and move into the future. This is not an easy conversation for a lot of people who have frankly been brung up in a certain way and are struggling to get on to the right side of history.

“But I also believe that this conversation is picking up speed, that it’s a healthy conversation and that where it leads is an understanding that all marginalized people need to stand together at a time when so many Americans in so many different ways, especially under this presidency, are coming under attack.”

Buttigieg was also asked if he thought a vote for Donald Trump, who he has said is a white nationalist, would be a racist act.

“At best it means looking the other way,” he said.