Jim Acosta and CNN are free to go write and publish whatever news or fake news they want . They are protected by the 1st Amendment. The 1st Amendment does not protect access to daily press conferences for media or opinion pieces. If it does then I assume you are ok with Infowars and Alex Jones having a press pass and access?
Infowars and Alex Jones shou,d be held to the same standards and protocols to granting access that other news organizations have to follow I can start my own newspaper and I won’t necessarily get access. The government can’t base that access based on nit liking the questions the reporter asks, or even if they are critical.