Fox News declared its “full support” for Sean Hannity on Tuesday, even as the network acknowledged that its executives were caught by surprise when the conservative commentator was named as a client of President Trump’s personal lawyer and fixer, Michael D. Cohen.

The backing from his bosses was not exactly a shock: Mr. Hannity is the top ratings draw at Fox News, and he has been unapologetic about what he described as an informal, “de minimis” arrangement with Mr. Cohen, whom he has vigorously defended on air. His Monday night show, hours after the relationship was revealed in a Manhattan courtroom, went on as scheduled.

But in the past, Mr. Hannity had run into trouble for crossing the line from commentator to activist — and Tuesday’s subdued reaction speaks to the new realities at Trump-era Fox News.

In 2010, Mr. Hannity was yanked from a Tea Party rally in Ohio after network executives objected to his appearance. “I don’t think we should be supporting the Tea Party or any other party,” Rupert Murdoch, the channel’s owner, said at the time.