In a new book, the Trump ally and potential running mate Kari Lake blows a “birther” racist dog whistle to supporters, claiming Barack Obama had a “mysterious past” when he ran for president – but does not mention that she donated to Obama in 2008 and reportedly campaigned for him door-to-door.

“The end of [George W Bush’s] presidency saw the complete and catastrophic collapse of the Republican party,” Lake writes, in Unafraid. “One Barack Hussein Obama, a man with a mysterious past and virtually no accomplishments on his résumé, ascended to the presidency.”

Rightwing extremist Lake, who supports Trump’s lie about voter fraud in 2020 and maintains despite repeated court defeats that her defeat for Arizona governor last year was also the result of cheating, also complains that the US media “swarm[ed] any independent journalist who attempted to give [Obama] a proper vetting”.

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The “birther conspiracy”, long championed by Donald Trump, holds that Obama was not a US citizen, having been born overseas to a Kenyan father, and thus should have been disqualified from becoming president.

Though disproven by Obama himself, the racist birther rhetoric lingers on the US right, including Islamophobic overtones invoked by Lake’s use of Obama’s middle name.

Lake’s book, Unafraid: Just Getting Started, is published in the US on Tuesday. The Guardian obtained a copy.

A long-time Arizona TV news anchor, Lake donated to the Democratic candidate for president in 2004 (John Kerry) and 2008 (Obama). She has said the Obama donation was made by her husband, while insisting there is nothing wrong with having been a Democrat before turning Republican.

In August 2022, the Washington Free Beacon, a rightwing site, reported that an unnamed former colleague at Fox 10 Phoenix said Lake also volunteered to door-knock for Obama.

The outlet said: “Lake’s alleged behavior doesn’t just contradict her rhetoric – network policy bars employees from campaigning for political candidates.”

Lake did not comment.

But she is now a voluble as well as a volatile presence on the hard right of the Republican party, refusing to concede defeat by the Democrat Katie Hobbs in the 2022 governor’s race and emerging as a possible vice-president pick should Trump win the nomination next year.

Earlier this month, Lake made headlines when she told Georgia Republicans prosecutors and the media were “going to have to go through me and … through 75 million Americans just like me” if they wanted to bring Trump down.

“And I’m going to tell you,” she said, “most of us are card-carrying members of the NRA [National Rifle Association]. That’s not a threat – that’s a public service announcement.

“We will not let you lay a finger on President Trump. Frankly, now is the time to cling to our guns and our religion.”

That was a reference to a famous campaign trail remark by Obama in 2008, when he said of working class voters in rust belt states: “They get bitter, they cling to guns or religion or antipathy to people who aren’t like them or anti-immigrant sentiment or anti-trade sentiment as a way to explain their frustrations.”

In her book, Lake blames the left for deepening social divisions in the US.

“In America we are not divided by religion, skin color, and the hundreds of other ways the left tries to separate us,” she writes. “We can have our differences, but it’s our patriotism and love for our country and our constitution that brings us together.”

But Lake shows little love for some members of the Biden administration she claims were only given senior roles because of factors including skin color.

Pete Buttigieg, she writes, “couldn’t even fix the potholes in South Bend, Indiana”, where he was mayor, but became “the United States transportation secretary just because he was gay”.

Of Karine Jean-Pierre, Lake says the White House press secretary “can’t string a sentence together” but is “in charge of briefing the American people on behalf of the president, just because she’s a black lesbian”.

Rachel Levine, the head of the US Public Health Service Commissioned Corps, is called “an overweight, middle-aged pediatrician” who got the job “because he decided he wanted to be a girl”.

Last week, Kelley Robinson, president of the Human Rights Campaign, testified to the Senate judiciary committee about the dangers posed by such rightwing invective.

She said: “On behalf of HRC’s more than 3 million members and supporters, I have come here today with a single message: the LGBTQ+ people of the United States of America are living in a state of emergency.”

The Guardian has contacted the HRC for comment about Lake’s attacks on Buttigieg, Jean-Pierre and Levine.