In the summer of 2016, government workers in Illinois received a mailing that offered them tips on how to leave their union. By paying a so-called fair-share fee instead of standard union dues, the mailing said, they would no longer be bound by union rules and could not be punished for refusing to strike.”To put it simply,” the document concluded, “becoming a fair-share payer means you will have more freedom.”The mailing, sent by a group called the Illinois Policy Institute, may have seemed like disinterested advice. In fact, it was one prong of a broader campaign against public-sector unions, backed by some of the biggest donors on the right. It is an effort that will reach its apex on Monday, when the Supreme Court hears a case that could cripple public-sector unions by allowing the workers they represent to avoid paying fees.More from The New York Times:A Supreme Court Showdown Could Shrink Unions’ PowerBack at Full Strength, Supreme Court Faces a Momentous TermSupreme Court Will Hear Case on Mandatory Fees to UnionsOne of the institute’s largest donors is a foundation bankrolled by Richard Uihlein, an Illinois industrialist who has spent millions backing Republican candidates in recent years, including Gov. Scott Walker of Wisconsin, Senator Ted Cruz of Texas and Gov. Bruce Rauner of Illinois.Tax filings show that Mr. Uihlein has also been the chief financial backer in recent years of the Liberty Justice Center, which represents Mark Janus, the Illinois child support specialist who is the plaintiff in the Supreme Court case.And Mr. Uihlein has donated well over $1 million over the years to groups like the Federalist Society that work to orient the judiciary in a more conservative direction. They have helped produce a Supreme Court that most experts expect to rule in Mr. Janus’s favor.The case illustrates the cohesiveness with which conservative philanthropists have taken on unions in recent decades. “It’s a mistake to look at the Janus case and earlier litigation as isolated episodes,” said Alexander Hertel-Fernandez, a Columbia University political scientist who studies conservative groups. “It’s part of a multipronged, multitiered strategy.”In doing so, these donors have not just brought labor to the brink of crisis but threatened the Democratic Party as well.Amid changes in the campaign finance landscape and the decline of private-sector unions, the party and its candidates have increasingly relied on major public unions for funding, including hundreds of millions of dollars in direct and indirect spending during the 2016 presidential cycle. Those unions include the American Federation of State, County and Municipal Employees, whose Council 31 is the defendant in the Janus case.A recent paper by Mr. Hertel-Fernandez and two colleagues may foretell what Democrats can expect if Mr. Uihlein and his fellow philanthropists succeed. It found that the Democratic share of the presidential vote dropped by an average of 3.5 percentage points after the passage of so-called right-to-work laws allowing employees to avoid paying union fees. That is larger than Democrats’ margin of defeat in several states that could have reversed…