A loose network of conservative operatives allied with the White House is pursuing what they say will be an aggressive operation to discredit news organizations deemed hostile to President Trump by publicizing damaging information about journalists. It is the latest step in a long-running effort by Mr. Trump and his allies to undercut the influence of legitimate news reporting. Four people familiar with the operation described how it works, asserting that it has compiled dossiers of potentially embarrassing social media posts and other public statements by hundreds of people who work at some of the country’s most prominent news organizations....