[Edit to cater to sensibilities]

Since we're not allowed to call people by their names, let me hash out a couple of points that, in my humblest perspective, should be mandatory knowledge for humanity in general. First one is don't talk about things you know nothing about, or if it that proves challenging to memorize, perhaps a well-known aphorism: "better to remain silent and be thought a fool than to speak and remove all doubt". The second lesson is that adults are responsible for their own education. People who proudly flaunt their ignorance and make it other's job to educated them produce the same revulsion as a pig gleefully wallowing in its excrement. It's dragging the rest of humanity down, it's a burden.

Now as for the specific context here, on if banning specific journalists from the White House is a first amendment violation: most definitely yes in this case.

The first aspect to it is what's known as the principle of "Viewpoint Discrimination".

This is very well established by the Supreme Court: when the government suppresses or punishes a message just because it disagrees with the speaker's point of view, it crosses the line into viewpoint discrimination. Extending this to the White House, from the moment you have a "public" event with an accreditation process, and you then proceed to ban access because of the "unfavourable coverage" (and this is a direct quote), this is clear cut viewpoint discrimination.

The second aspect is the argument that White House press conferences are akin to designated public forums.

While the President is not legally required to hold press conferences or call on specific reporters, if a public forum is established for the press corps, the administration cannot selectively expel certain journalists as a tool for censorship or intimidation.

The third aspect is existing case law and past rulings:

Sherrill v. Knight (1977): The D.C. Circuit Court of Appeals ruled that the White House cannot deny press credentials arbitrarily. It established that the White House must have clear, published, and consistent standards for granting or denying access, and must provide due process.

CNN v. Trump (2018): When the White House revoked Jim Acosta's "hard pass" following a... rough press conference, CNN sued. A federal judge granted a temporary restraining order forcing the administration to restore his access, citing Fifth Amendment due process violations. Unfortunately the judge pussied out of also explicitly flagging First Amendment free speech rights on that one, but the White House folded and reinstated the credentials. Ultimately, the most important aspect here is that this is blatantly unacceptable behaviour.

If you do feel it is justified, apply a litmus test: would it still be acceptable if it was done by [insert someone you hate here]. For example, would it have been acceptable for Biden to ban a Fox reporter because of bad coverage?

The final conclusion is that this is not even something that the courts should have to rule on: people should be out in the streets shouting for their freedom and against the massive assault they're under. Rights are something that need to be fought over, as they're never granted freely, and relying on the Courts alone to uphold them will fail.