UCLA law professor Eugene Volokh said the White House doesn’t necessarily need to have a powerful reason to keep Mr. Acosta out. More recent First Amendment case law suggests that the president could win by convincing a judge that the decision was merely reasonable, according to Mr. Volokh.

The key for the White House, he said, is showing that it took action against the CNN reporter not based on his reporting or critical views about Mr. Trump but because of his conduct at news conferences…

Ken White, a free-speech advocate who writes the Popehat legal blog, said CNN’s suit “is very plausible.” What’s less clear, he said, is “what role a court will take into probing the sincerity of the administration’s stated reason.”

Drilling into motives could require a lot of discovery and the production of emails and other evidence. But with CNN filing an emergency motion asking Judge Kelly to immediately restore Mr. Acosta’s credentials while the case is pending, the court doesn’t need to wait for the litigation to unfold. Judges tend to have a lot of leeway in determining whether to grant a preliminary injunction like the one CNN is seeking.