Ignoring Trump (which I highly recommend doing in all situations where it's remotely feasible), I have to say I think* it's well within the bounds of the First Amendment to block people on social media, even from official government accounts.
First of all, while the 1A gives us the right to "petition the government for redress of grievances," elected officials have always been allowed to willfully and preemptively and selectively and even algorithmically ignore those petitions.
And if we start from the premise that every government account on a privately owned website is the same as the public square for free speech purposes, you end up on a pretty steep slippery slope to absurdity. I'm allowed to say that Ryan Zinke is a shitty little weaselfucker if I want without the FBI dragging me from my bed in the middle of the night. I can stand in the town square and proclaim it all day long (provided I'm obeying other laws--e.g., I can shout it, but I can't use a 1,000-watt amp to make it rattle the glass a mile away). I can write a note to every member of Congress saying "Please do something about this shitty weaselfucker."
But do I have a right to post the 10,000-word Ryan Zinke Is A Shitty Weaselfucker Manifesto on every NPS facebook post? What about 140 characters at a time on my local school board's Twitter feed? If not, why not? Where do you draw the line? I think the common-sense answer (and you might be surprised at how often the courts choose those in 1A cases) is that the person or entity convening the forum gets to make that call, and if people have a problem with being excluded, there are political remedies.
I mean, heck, Twitter itself bans all kinds of speech that is constitutionally permissible in the public square. I can do public readings of The Turner Diaries or The Protocols of the Elders of Zion if I want, but I can't Tweet them, even if I think it's vitally important that Trump know about them. (As I'm sure many of his supporters do.)
A smart and fair-minded politician (I said we were ignoring Trump!) would bend over backwards to craft a policy that allowed constructive dissent while banning spam, abuse, copypasta, flooding, brigading, sniping, off-topic posts, etc. In other words, the same kind of thing halfway-decent blogs do. (And no internet comment forum is better than halfway decent.) But that's just good-governance stuff--I really doubt a court would force the issue.
*not a lawyer! thhhhpt