The Mercers, who rarely grant interviews, declined through a spokesman to comment. Mr. Mercer, 70, a mathematician and competitive poker player who spent his early career at I.B.M., joined Renaissance in the 1990s and rose to become the co-chief executive, earning hundreds of millions of dollars along the way. Today, he and his wife, Diana, live on a sprawling estate on Long Island’s North Shore where, according to court records, he installed a $2.7 million model railroad set (and later sued the vendor for overcharging him).

Like many elite donors, the Mercers shun mainstream media attention — even while financing alternative outlets that provide content for conservative activists. That includes not just Breitbart, but also the self-described watchdog organization Media Research Center and the Government Accountability Institute, home to Peter Schweizer, the author of “Clinton Cash,” a book examining the Clinton family philanthropies. (Mr. Bannon co-founded the institute and Ms. Mercer, 42, has served on its board; she also co-produced a documentary based on the book and released last month, just before the Democratic National Convention.)

They have given to libertarian organizations, such as the Cato Institute, and political organizations like the Club for Growth, which spends millions of dollars each election cycle in Republican primaries, hoping to promote orthodox conservative policies on taxes and spending. The Mercers are also significant donors to the sprawling political network overseen by the political activists Charles G. and David H. Koch, which is also libertarian-leaning.

But unlike the Koch brothers, who remained neutral in the Republican primary and have said their organizations will focus on congressional races this fall, the Mercers were deeply involved in the Republican nominating battle this year. And they have shown a taste for more bare-knuckled and populist politics than most of Mr. Mercer’s fellow hedge fund magnates.

The family originally backed Senator Ted Cruz of Texas, a more traditional conservative but one who, like Mr. Trump, is disliked by much of the party establishment. During the early phase of the campaign, Mr. Mercer donated $13 million to a super PAC supporting Mr. Cruz. In doing so, he broke with many peers in the elite donor world, who looked to candidates like Jeb Bush or Senator Marco Rubio of Florida.

The Mercers maintained close control over the group’s purse strings, installing Ms. Conway to oversee the group and coordinate with several other pro-Cruz groups, an unusual move for a super PAC. During the Republican primary, the group ran ads questioning Mr. Trump’s conservative credentials, hoping to outflank Mr. Trump.