Govt. May Be Violating First Amendment by Blocking People from Social Media

In November 2017, the ACLU of Washington sent a letter to all Washington state lawmakers, warning they could be violating the First Amendment when they block people on their social-media accounts.

The ACLU letter describes those pages as “limited public forums” protected by the First Amendment, and says lawmakers can regulate speech such as vulgar or off-topic posts there.

“But viewpoint discrimination — for example, removing posts or blocking particular users entirely on the basis of the point of view expressed — is never permissible since it violates the First Amendment right to free speech,” the letter says.  (The Olympian, July 28, 2018)
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Allowing a government actor to ban critics from speaking in public forums would silence and chill dissent, warp the public conversation, and skew public perception. And enabling government actors to block critics from petitioning them for services or seeing public information would mean punishing them for speaking out or holding critical views.

As a government agency if you establish a social media account, you should never block anyone from viewing that social media. If you allow comments to be made to your social media page, then you must allow all comments to be posted (except as noted above those which are "vulgar or off-topic").