CNN actually has a good foot in court right now since the there is already precedent from a 1977 court decision that the White House must follow a specific process to deny press passes (which the white house didn't follow)
https://openjurist.org/569/f2d/124/sherrill-v-h-knight
"White House press facilities having been made publicly available ... the protection afforded news gathering under the first amendment... requires that this access not be denied arbitrarily or for less than compelling reasons."
That case is about a denial of an application for a press pass, based on a Secret Service recommendation that it not be issued for reasons not disclosed to the applicant. The Acosta situation involves a revocation of an existing pass, for specific conduct witnessed by the public and during a Presidential press conference. These are easily distinguished factual situations. CNN wasn't banned. One poorly behaved reporter was.