Two years ago, hedge-fund investor Robert Mercer and his daughter Rebekah had the president’s ear. Now, on the eve of midterm elections, a different group of Wall Street executives enjoys access to the Oval Office.

The Mercers are playing a less-important role backing conservative politicians, according to campaign finance filings and people close to the matter, even as a handful of other finance executives boost their contributions during the latest election cycle.

“They’ve...