The judge ruled the White House had violated due process by banning Acosta.

CNN, however, had requested a ruling saying that Acosta more or less had a constitutional right to a press pass, and that the First Amendment guaranteed CNN and its reporters access to the White House press conference room.

Judge Timothy Kelly disagreed. According to the Washington Post:

In explaining his decision, Kelly said he agreed with the government's argument that there was no First Amendment right to come onto the White House grounds. But, he said, once the White House opened up the grounds to reporters, the First Amendment applied.

On the due process issue, Kelly is mostly right on this one. But Kelly gets it wrong when he says that the First Amendment potentially applies wherever the White House has opened up access to reporters overall.