The Rev. Clenard Childress, of Montclair, N.J., speaks at an anti-abortion rally in San Francisco, Saturday, Jan. 22, 2005. (DINO VOURNAS/ASSOCIATED PRESS)

Eldon Bell, a retired Air Force officer and physician, is making no plans to see Barack Obama’s second inauguration, in part because Bell considers the president arrogant and dishonest, but more so because Bell is not yet persuaded that the swearing-in will occur at all.

“Whether I watch depends on who’s being inaugurated,” says Bell, 78. “If it’s this guy, probably not, because I don’t pay much attention to illegitimate things.”

At this late date, Bell and his fellow believers in the notion that Obama was born overseas or is otherwise ineligible to be president still expect some court somewhere to buy into one of their theories. After more than 100 court cases, no judge has.

Even after Obama convincingly won reelection despite four years of low popularity ratings, a sluggish economy and a highly motivated opposition, advocates of various counterfactual theories about the president — he’s a foreigner, he’s a Marxist, he’s a Muslim — say they’re sticking to their fight.

“This inauguration is a mistake and those who permit it to happen will have to live with their own consciences,” says Bell, a former Washingtonian who retired to South Dakota.

Most Americans have moved on from earlier dalliances with denials of the president’s biography. National opinion polls have shown increases over the past three years in the percentage of Americans who agree that Obama was born in the United States and that he is a Christian. But a persistent minority — between a tenth and a fifth in most polls — still believe he is Muslim, foreign-born or a socialist.

Those voters tend to be vehement opponents of Obama, and on Inauguration Day, they will not be at the party — and they’re still searching for ways to have the president declared illegitimate.

“Let’s face it, this is a man very deep into an ideology that is not American,” says the Rev. Clenard Childress, a New Jersey minister and antiabortion activist who says black and white voters alike returned Obama to office “to feel better about ourselves and get the guilt of racism off us.”

Childress says it’s 50-50 that Obama is a Muslim who was born in Kenya: “But what I really care about is do we have the same values? Do you believe in the sanctity of life? Do you believe in marriage as being between man and woman? And this president does not.”

Just because the election is over doesn’t mean the confrontations of the first term will end, Childress says. In addition to the fiscal battles on Capitol Hill, the minister says, social issues will keep Obama opponents fired up, starting with next month’s antiabortion rally on the Mall and continuing with court and political battles over same-sex marriage.

“There will never be more contentiousness than in the next two years,” he says. “I told my congregation: Just strap yourselves down, it’s going to be nasty.”

Those who monitor anti-Obama movements say the inauguration will do nothing to quiet the rapids. “The rhetoric since the election has actually gotten more vicious,” says Kevin Davidson, better known as “Dr. Conspiracy,” his handle on his Web site, Obama Conspiracy Theories, which keeps tabs on those who declare Obama’s presidency illegitimate.

Davidson, a retired software developer in South Carolina, has been predicting for four years that hardcore anti-Obama agitation would dissipate, but it keeps going, driven, he believes, by anti-black sentiment. “I’ve seen more openly racist remarks since the election,” he says. “Before November, they were careful to control the racist language because they were trying to persuade people to vote against him. Now they sort of don’t care.”

Hard-core opponents say that even without another election, they will keep up their efforts to end Obama’s tenure. “We have to think about impeachment for abusing executive power,” says Cliff Kincaid, who runs America’s Survival, a collection of Web-based groups portraying the nation as threatened by socialism, the United Nations and liberal culture. “The Republicans seem not to realize that Obama is a Marxist who wages class warfare and could not qualify for a sensitive government position based on his associates and his character.”

Kincaid, based in Owings, Md., recognizes that impeachment is a long shot, so he is focusing on pushing the GOP rightward. “We can survive Obama,” he says, “but is there another Reagan-like conservative who can lead the charge? Romney refused to run as a conservative. We had a failure of conservative candidates and conservative media, not of conservative philosophy.”

Although many Americans have thought about whether the president’s approach to health care and the role of government equates to socialism — “socialist” was the most looked-up word in the Merriam-Webster online dictionary in 2012 — polling indicates more widespread support for the conclusion that Obama is what he has called himself, a pragmatist. Before his first inauguration, he said that “what is required is a new declaration of independence, not just in our nation, but in our own lives — from ideology and small thinking. . . .”

Still, Obama’s more severe critics see him as highly ideological. Francis Cianfrocca, a New York cybersecurity entrepreneur, believes the president is determined to limit freedom and wealth. “He called people like me ‘fat cats,’ ” says the successful businessman. “What are we supposed to do with that? A lot of the personalization of the opposition to him comes from his saying personal things against capitalism, business people and Republicans.”

Although Cianfrocca thought of Obama as “a thoroughgoing socialist looking for wholesale reconstruction of the economy,” the president’s reelection persuaded the businessman that “the country is with him and that gives him tremendous moral authority.”

Cianfrocca’s disagreements with the president are mainly philosophical; he believes the country will right itself and flourish again within a decade. Many birthers and other hardcore anti-Obama activists, in contrast, see the president as the final architect of the collapse of American power.

“I despair for the future of our country,” says Bell. “He’s an emperor with no clothes.”

Even if the birther movement has lost some steam since Obama released his birth certificate in 2011, Davidson sees evidence that birthers are diversifying into other anti-Obama issues, using their Web sites and radio shows to focus attention on the next phase of the health-care debate, the attack on a U.S. diplomatic post in Libya and the latest Cabinet nominations.

Although Dr. Conspiracy is obsessed with tracking the birthers — before he retired, he worked on the software that state governments use to manage vital records, and that got him interested in the debate over Obama’s birth certificate — he is not one of them. After engaging with thousands of people who believe Obama has committed identity fraud, he says, “I know two examples in the entire country of birthers who changed their views. It’s just in the nature of believers that you can’t back down.”

Conspiracy theories have been an undercurrent in American politics since the birth of the republic, but after decades in which such ideas could be hawked only through obscure newsletters and shortwave radio, the Internet and cable TV have made it far easier to connect with like-minded souls.

From inside the information silos of left and right, Obama can seem to be the subject of the most virulent hatred of any modern president. But that’s been said of the past three occupants of the White House. Hillary Clinton said during her husband’s presidency that a “vast right-wing conspiracy” was out to get him, and an energetic network of Enemies of Bill questioned his qualifications and honesty from long before his candidacy through his impeachment in 1998.

George W. Bush and Richard M. Nixon hold the modern records for highest disapproval ratings in Washington Post-ABC News polling, but such surveys don’t capture the relatively small numbers of people who turn unhappiness with a president into a dyspeptic worldview.

“There’s a certain world of people who move from one conspiracy theory to the next,” says Bill Bryan, proprietor of The Fogbow, a Web site devoted to debunking anti-Obama movements. “Obama is perfect for them. They just hate him so much, and the election won’t end that. They really believe that one day soon, he’ll be declared an illegal president and Obamacare will vanish with a poof and Sotomayor and Kagan will have to leave the Supreme Court.”

“I got sucked into their vortex,” Bryan says, “but when I run into normal people, like waiters at a restaurant, only half of them have even heard of birthers, so I take comfort in that.”