For publishing "fake news"?
Can anyone remember when a president was so anti First Amendment?
Nixon and Johnson.
That's possible, but it doesn't match my recollection. Could you provide some examples of things Johnson said or did to support your claim? Johnson certainly wasn't happy that he and his administration were criticized in editorials and that many news stories of the time did not make him or his administration look good, but I don't recall any time he threatened, explicitly or implicitly, to use government powers to close down media outlets which were critical of him.
Nixon comes closer. According to
the Washington Post, some of Nixon's allies tried to compete for the licenses of local tv stations. That's certainly something worth mentioning as part of a discussion about Trump's statements in relation to the media, but it's not the same. Nixon's chief media problem was with the Washington Post. If Nixon had attempted to sabotage, close down, take over, prosecute, or take other (overt or covert) government action against the Washington Post, or any other national news media outlet of the time, that would be comparable to Trump's implicit threat to take government action against NBC. Nixon may have made such threats (publicly or privately) but I don't recall them. So if you could provide examples to support your claim it would be helpful.
Wartime presidents tend to be adversarial with the press. Roosevelt and Wilson had their moments too. Wilson pushed through the Sedition Act which essentially criminalized publishing anything against the war. FDR issued an executive order creating a Censorship Board during the war.
Yes, Wilson is a very good example of a president taking as strong an action against the first amendment as Trump is threatening. The Sedition Act of 1918 was used to prosecute (and imprison) people for speaking out against the war and the draft. (As I recall, that's where the oft-quoted line in a supreme court decision about shouting fire in a crowded theater comes from. The justice was equating opposing the draft during wartime with shouting fire in a crowded theater.)
Roosevelt I'm not so clear on. I think censorship of news stories during active war time to prevent classified information relevant to the war effort from being made public can be justifiable, and that government action to make sure secret information stays secret is different than government action to prevent media from saying things critical of the government and government policies. Wilson's actions (and Trump's threats) are aimed at silencing criticism; it's possible Roosevelt's actions had a similar purpose but if so it's not something I'm aware of.
For example, I'm familiar with government checking into some comic book and science fiction stories which related to atomic weapons and requesting these be altered or not published, because they didn't want attention called to the real-world work the US was doing then on developing atomic weapons; I'm not familiar with any government actions aimed at suppressing media criticism of the internment of the Japanese.
As I recall Roosevelt was quite tolerant of the media criticism he received, such as the weekly anti-Roosevelt broadcasts of Charles Coughlin. No government action that I can recall was taken against Coughlin even though he routinely attacked Roosevelt and defended Nazi actions; it was the Catholic Church which finally cracked down on Coughlin after war had been declared and they could no longer overlook his actions. So if you could provide examples of Roosevelt taking or threatening actions to shut down media criticism of him that would be helpful in seeing if he really is comparable to Trump in this regard. (But whether Roosevelt actually is or not, I do agree with you that Wilson is.)