By Alex Swoyer

President Trump hadn’t even had a chance to officially release his new list of judicial nominees this month before a progressive advocacy group issued a statement blasting one of the picks for having ties to The Federalist Society.

A national network of conservative and libertarian-leaning lawyers and scholars, the society has become the new bogeyman for the left, which sees it as the main source of shock troops in a Republican strategy to deploy an army of Antonin Scalia-like judges to invade the federal courts and the Justice Department.

Democrats already tried to derail the nominations of Supreme Court Justice Neil M. Gorsuch and Judge Amul Thapar in part because they were on the list of 21 potential nominees released during the campaign by Mr. Trump — a list The Federalist Society helped to craft.

Judge Thapar had to overcome universal Democratic opposition to win his seat on a federal appeals court, while Democratic antipathy to Justice Gorsuch forced Republicans to alter the Senate’s rules by curtailing the power of the filibuster to get him installed.

“We probably can’t support any nominee vetted by The Heritage Foundation and The Federalist Society,” Senate Minority Leader Charles E. Schumer, New York Democrat, said during the debate over Justice Gorsuch.

For liberals, the society has replaced the billionaire Koch brothers as the dark force operating behind the scenes, working to foil Democrats’ agenda. But that dark portrait is laughable to Leonard A. Leo, executive vice president of The Federalist Society, who says its goals are no secret.

“The institution is not embarrassed by the fact that we want a judiciary that will say what the law is and not what it should be, so this idea that somehow we are in the dark shadows of Washington trying to pack the courts is really utter nonsense,” Mr. Leo said. “Some senators just don’t really understand who we are and what we do.”

Mr. Leo took a leave of absence from the society to help Mr. Trump fill the Supreme Court vacancy left by the death of Justice Scalia last year. He rejoined the society after Justice Gorsuch’s confirmation.

So far Mr. Trump has selected three of the 21 names on his list for advancement: Justice Gorsuch, Judge Thapar and Colorado Supreme Court Justice Allison Eid, whom the president tapped June 7 to fill the seat Justice Gorsuch vacated on the U.S. Court of Appeals for the 10th Circuit. She was the nominee who immediately faced pushback from the Alliance for Justice, which said she must have passed The Federalist Society’s litmus test regarding opposition to gun safety and abortion rights.

Yet another of Mr. Trump’s June 7 picks, Stephanos Bibas, has been a regular panelist at Federalist Society conferences. Others with society ties include Noel Francisco, Mr. Trump’s pick for solicitor general; Rachel Brand, the newly confirmed associate attorney general; and Steven Engel, Mr. Trump’s pick to be head of the Justice Department’s Office of Legal Counsel.

Democrats tried to filibuster Ms. Brand, and appear ready to attempt to block Mr. Francisco and Mr. Engel when their nominations reach the floor.

Mr. Leo said his organization is a “natural pipeline for talent,” so it’s not surprising for Mr. Trump to select from its members, who are committed to an originalist, textualist form of judicial interpretation.

‘Open debate’ group

Founded more than three decades ago to counter the liberal orthodoxy that flows through law schools and the American Bar Association, The Federalist Society has included Scalia, Justices Clarence Thomas and Samuel Anthony Alito Jr. and Chief Justice John G. Roberts Jr.

The society operates chapters at major law schools and hosts gatherings where legal issues — both hot topics and arcane points of law — are debated. Liberal legal stars often appear at the conferences as part of the debate.

The Federalist Society also analyzes high-profile court cases, making its experts available for reporters.

But Democrats say the organization’s troubling activity comes in the judicial selection process, where the society has been influential in shaping the picks for Republican presidents.

During Justice Gorsuch’s confirmation hearing, Sen. Patrick J. Leahy told him it’s a problem that the president “outsourced your selection for the far-right, big money, special interest groups.”

“They have an agenda. They’re confident you share their agenda. In fact, the first person who interviewed you for this nomination said they sought a nominee ‘who understands things like we do,’” said Mr. Leahy, Vermont Democrat.

Mr. Leahy similarly criticized Judge Thapar, who during his confirmation hearing described the organization as an “open debate” society.

Sen. Richard J. Durbin said it’s more nefarious than that.

“Aside from the three or four families or groups that are major contributors to the Republican Party, there’s a whole group of dark money contributors who are not disclosed, so this argument that this is just a debating society, which is what Judge Thapar called it, I think really doesn’t pass the laugh test,” the Illinois Democrat told The Washington Times.

Mr. Leo says there’s nothing private or secretive about his group, who is a member and what it stands for: “Our statement of purpose is right there for everybody to see. It’s basic constitutional law and civics from high school. Our funders are disclosed in the annual report.”

Because The Federalist Society is a 501(c)(3) nonprofit group, its donors can remain anonymous. But it does publish its financial reports on its website each year.

From 2013 to 2015 the Koch brothers and the U.S. Chamber of Commerce were among the most notable names that routinely donated more than $100,000 to the organization. Kellyanne Conway, Mr. Trump’s senior adviser, and her husband routinely donated more than $50,000 during each of those three years, as did the Anschutz Family Foundation, headed by Philip Anschutz, a billionaire Justice Gorsuch represented as a lawyer in the early 2000s.

Chevron Corp., Delta Air Lines, BP America Inc., Google, Pfizer Inc. and Microsoft were among several corporations that have donated to the society since 2013.

During those same years, more than 30 donors giving more than $100,000 chose to remain anonymous.

Society of influence

Josh Blackman, a law professor at South Texas College of Law who often speaks at Federalist Society events, said the network of the group’s lawyers is so large that some inside the Trump administration are even members.

“If you are a prominent respective lawyer who is on the conservative side of the spectrum, the odds are you will be a member of the society,” Mr. Blackman said. “This is not some sort of vast right-wing conspiracy, as some are trying to paint it.”

Elizabeth B. Wydra, president of the left-of-center Constitutional Accountability Center, said she’s enjoyed appearing on panels at Federalist Society events. But she questioned the value of the organization’s judicial recommendations — such as society member Damien M. Schiff, a May 8 pick to serve on the U.S. Court of Federal Claims.

“On one hand, the confirmation of Justice Gorsuch is strong evidence of The Federalist Society’s influence on the judicial nomination process, but on the other hand, some Trump judicial nominees — for example, Damien Schiff, who called Justice Anthony M. Kennedy a ‘judicial prostitute’ — indicate a real lack of judgment on the part of this president and the people advising him,” Ms. Wydra said.

Marge Baker, vice president at People For the American Way, said The Federalist Society has long had influence in shaping Republican judicial picks, but said that influence has grown under Mr. Trump.

“This administration — more so than [any] I [have] ever seen — is outsourcing that almost sacred responsibility,” she said.

Curt Levey, president of the Committee for Justice and an attorney for FreedomWorks, equated the influence that the ABA has had on the courts to that of The Federalist Society.

“Most Democratic judicial nominees belong to the ABA, and the ABA rates judicial nominees — something The Federalist Society does not do — yet it would be inaccurate to say that the ABA selects nominees,” said Mr. Levey. “Instead, the ABA and Federalist Society are one source of information for an administration trying to fill many dozens of judicial vacancies across the country.”

Liberals have their own legal organization, the American Constitution Society, which held its national conference in Washington last week and attracted Democratic senators and Justice Stephen G. Breyer.

But it has not gained the sort of influence — or the stigma among political opponents — as that of The Federalist Society.

“What’s really unusual is to outsource the process,” said Caroline Fredrickson, president of the American Constitution Society. “Certainly we were consulted by the Obama administration as to people who would be good choices, but they consulted many different sources, and they didn’t give outside organizations the role.”

Federalist Society member Steven R. Klein said Democrats’ attacks don’t discredit the organization.

“It was stupid when they tried to do this during Justice Roberts and Justice Alito — during those confirmation hearings.