I think it's wildly stupid that the President would block people on Twitter, if only from a PR POV (particularly given the existence of muting), let alone read his replies in the first place, but it's impossible to create a coherent case for why blocking someone on Twitter infringes on free speech.
The government cannot prevent people from commenting and discussing the government's speech (through retweets etc). Logging out is not a solution. Sure, you can talk in person, or on Facebook, or even copy-paste the content. But you couldn't retweet, and thus you were blocked from participating in the public discourse.
Turns out, the government can't interfere with private citizen's ability to engage in public discussion about the government, even if it's just on some dumb site like Twitter.
In fact, if his account was private, and it was only discussion for his personal friends or whatever, then there wouldn't even be an issue. The public nature of the account is exactly why he can't block people. It would be like the government sending an official request to Fox News to block democrats from appearing on the air. Sure, they could just watch on TV, but the government has essentially told a private entity they have to block certain citizens from speaking on their platform. It doesn't matter if Fox News would agree to it or not, the government cannot even ask for it.
I thought I took the broadest possible view of free speech, seriously. I just honestly can't get to the idea that there is a First Amendment right to retweet from your preferred account (which is the only thing that a block actually prevents) or that not being able to retweet from your preferred account actually impacts the ability to participate in public discourse.
Sidebar: Twitter should be terrified of this, right? This is treating behavior on a private company's site as protected speech. I know that right now it's limited to the government, but it's now a much smaller leap to "Twitter is protected speech" in the same way that "putting up a flyer in a public square is protected speech".
All the social media companies should be quaking in their boots. For example, Facebook disallows convicted sex offenders from their service. If these free speech distinctions continue to move in this direction, courts will eventually force these platforms to allow everyone.
By the President and his administration’s own description, it is an official tool of government. From the ruling: “The President and multiple members of his administration have described his use of the Account as official.”
From a practical perspective, it is the only way the administration addresses the public since they block any honest journalist from an interview and they have essentially cancelled press conferences.
Not once he started issuing policy (https://twitter.com/realDonaldTrump/status/89019398158544486...) and firing people (Tillerson) via it.
Blocking people as the president is closer to limiting the free speech of citizens than exercising his right to free speech.