Did The White House Violate the First Amendment by Barring AP Reporters and Photographers?

Over the past few days, AP News has been barred from a few events at the white house and an air force one flight. This is the result of AP News referring to the Gulf of Mexico/America/etc. by its internationally-recognized name.

AP News has called this a violation of the first amendment and brought up fears of this being a precedent for banning other left-leaning media organizations, while the White House has defended its decision. Here's AP News' story on the ban, and here's another story from NPR covering responses from both the WH and AP. For a right-leaning source, here's Fox's story about the matter as well.

This ban comes a few months after both Elon Musk and Donald Trump have called to defund NPR and a few weeks after several major news outlets were removed from the Pentagon. Under the Biden administration, updated 2023 press guidelines resulted in more than 440 reporters losing their press passes.

I'm interested to hear what other's thoughts are on the matter. Was this a violation of the first amendment or a justified decision by the Trump administration?