In his final presidential debate with Hillary Clinton, Donald Trump said the Supreme Court would “automatically” overturn Roe vs. Wade once he became president, “because I am putting pro-life justices on the court.”

Now Trump has a chance to carry out that prediction with his announcement, due Monday, of a nominee to succeed retiring Justice Anthony Kennedy, the court’s swing vote on abortion, gay rights, guns and other issues. When reporters wondered whether he would seek out prospective nominees’ opinions on Roe, the 1973 ruling that legalized abortion, the president said, “That’s not a question I’ll be asking.”

In all likelihood, he won’t have to.

Trump’s announced list of 25 candidates for Kennedy’s seat, which he has reportedly narrowed to two or three finalists, was selected by the Federalist Society, a group started by law students in in 1982 to move the courts to the right. It has grown into a network of 60,000 academics, legislators, law clerks and judges who make their voices heard on campuses, in opinion forums and in Republican presidential administrations. Financial backers include Google and Chevron, as well as the conservative billionaire Koch brothers.

The prime mover has been Leonard Leo, the society’s executive vice president. He recently went on leave to advise Trump on the Supreme Court nomination, working alongside White House counsel Don McGahn, also a Federalist Society member. Leo played the same role last year when Trump — who had promised during his campaign to let the Federalist Society pick his judges — made his first Supreme Court selection, Federalist Society member Neil Gorsuch.

Two other conservative justices, Clarence Thomas and Samuel Alito, were both Federalist Society members. Chief Justice John Roberts served on a Federalist Society board. The organization’s original academic advisers were future Justice Antonin Scalia, Trump’s self-described model jurist, and fellow archconservative Robert Bork.

And it’s not just the Supreme Court where the society is influential, but in the screening and selection of federal judges at every level, said Amanda Hollis-Brusky, a Pomona College political science professor and author of “Ideas with Consequences: The Federalist Society and the Conservative Counterrevolution.”

Trump “has largely outsourced the entire operation to the Federalist Society,” Hollis-Brusky said.

The society disavows any formal positions on social and political issues, declaring on its website that its only policy priority is “making sure that the principles of limited government embodied in our Constitution receive a fair hearing.” But Leo has called abortion “a threat to human life.”

“There are competing constituencies within the conservative coalition,” Hollis-Brusky said. “Some care very deeply about the abortion issue, others about deregulating businesses. ... Leo is the only one who put the (Supreme Court) list together. To him, the abortion issue is extremely important.”

That seems to be reflected in the records of some of Trump’s reportedly leading candidates, all Federalist Society members.

Brett Kavanaugh, a former Kennedy law clerk appointed by George W. Bush to the federal appeals court in Washington, D.C., in 2006, wrote an opinion last year refusing to let a 17-year-old girl leave an immigration detention facility in Texas to get an abortion. He said the Trump administration was entitled to maintain a policy of “favoring fetal life” and keep the girl in custody until a federal agency found an acceptable sponsoring agency to house her.

The full appeals court later overruled Kavanaugh and allowed the abortion. Some antiabortion groups say Kavanaugh should have gone further and joined a conservative colleague who argued in dissent that undocumented minors have no constitutional right to an abortion.

Another reported finalist, Amy Coney Barrett, a former Scalia law clerk, has not considered any abortion cases in her brief tenure on the Seventh U.S. Circuit Court of Appeals in Chicago, to which Trump appointed her in November. But she is a devout Catholic who belonged to University Faculty for Life as a Notre Dame law professor from 2010 to 2016, and has been quoted as saying that “life begins at conception.”

In 2013, Barrett wrote a law review article saying the Supreme Court’s tradition of following precedents set by previous decisions was “not a hard-and-fast rule in the court’s constitutional cases” — noting, for example, that Kennedy’s 2003 ruling striking down criminal laws against gay sex had overturned a 17-year-old precedent.

She went on to refer to “the public response to controversial cases like Roe” as a rejection of the idea that past precedents should decide “a divisive constitutional struggle.” But in a speech that same year, she predicted the Supreme Court would not overturn Roe vs. Wade.

Barrett also co-wrote a 1998 law review article suggesting that Catholic judges would have to disqualify themselves from death penalty cases because of the church’s opposition to capital punishment. By contrast, Scalia, her former boss, wrote a 2002 article in a Catholic journal saying the church had no official, binding position on the death penalty, and implying he would have to resign from the court if the church ever took such a stance.

Sen. Dianne Feinstein, D-Calif., cited Barrett’s article during her October 2017 confirmation hearing to suggest that as a judge, she would be beholden to her religion. “The dogma lives loudly within you,” Feinstein said — words that had the unintended consequence of galvanizing conservative religious support for Barrett and possibly propelling her to the top of the Supreme Court candidates list.

A third reported finalist, Raymond Kethledge, another former Kennedy law clerk, hasn’t heard any abortion cases since Bush named him to the Sixth U.S. Circuit Court of Appeals in Cincinnati in 2008. But he formerly served as a legal adviser for Sen. Spencer Abraham when the Michigan Republican sponsored antiabortion legislation.

Kethledge has been more prominent as a firearms advocate, telling a Federalist Society gathering in 2016 that courts had been too stingy in their interpretations of Scalia’s 2008 Supreme Court ruling declaring the right to keep a handgun at home for self-defense.

Kavanaugh has taken a similar position, arguing that the Constitution protects the right to own semiautomatic rifles. But he may be best known as an author of Independent Counsel Kenneth Starr’s 1998 report calling for the impeachment of President Bill Clinton.

With a 51-49 Senate Republican majority, and Sen. John McCain, R-Ariz., probably unable to participate because of brain cancer, Trump’s nominee will need support from every Republican if Democrats all vote in opposition. The most likely swing votes appear to be Susan Collins of Maine and Alaska’s Lisa Murkowski, the only Republican senators who support abortion rights.

Murkowski has said she would consider the abortion case as one of many factors in voting on a court candidate. Collins, in recent television interviews, said she would not support a nominee who showed “hostility to Roe v. Wade” and would insist that any court pick declare a “respect for precedent.” That would seem to suggest a problem with statements like Barrett’s about abortion and the 1973 ruling.

But Hollis-Brusky said the nominees, schooled by Leo, know how to avoid such questions during the confirmation process.

She recalled the Federalist Society’s interactions with Bush. When Justice Sandra Day O’Connor retired in 2005, Bush’s initial choice was his friend and White House counsel, Harriet Miers. Leo, then in the White House, supported the nominee, but other Federalist Society members were prominent in a conservative backlash. They warned that Miers, with virtually no public record on contentious issues, could prove to be a rerun of David Souter, the George H.W. Bush appointee who wound up aligning with the court’s center-left bloc.

Miers withdrew under pressure, and Bush then nominated Alito, a Federalist stalwart. He was confirmed 58-42, with a handful of Democratic votes, after denying any ideological bias and sidestepping questions on abortion.

“I would bet my child’s college education that any nominee Trump puts forward will not say how they’re going to rule on a case that would overturn Roe v. Wade,” Hollis-Brusky said. “We learn very little during the hearings.”

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter:@BobEgelko