“If it weren’t for Charlie Kirk, I would not be the vice president of the United States,” J. D. Vance said as he hosted “The Charlie Kirk Show” last week. This may well be true: Kirk lobbied for Vance to get the vice-presidential nomination. It’s also a reflection of how deeply Donald Trump’s White House is intertwined with a thriving ecosystem of partisan podcasters who amplify his agenda — and help set it. In the past decade, American public life has undergone two major transformations: The MAGA movement has swallowed the Republican Party whole. And influencers such as Kirk have...