Re: I am curious to see how this works out.
Irrelevant to the existing case, which is about government officials using a particular feature of a social-media platform for what can be seen as official statements, and whether such officials can block readers or respondents.
In the Facebook case, Randall had a Facebook page she treated as an official government forum. The court ruled she cannot block someone from that page, because it serves as such a forum.
In the Twitter case, the courts have ruled that Trump is using his Twitter account as an official channel of public communication, and so he is not allowed to block people from it. Same reasoning: when acting as a public official, your right to restrict access to your public communications is limited.
Your example says nothing about where the communication is taking place, and in particular whether it might reasonably be considered an official channel. More importantly, in this context, you're not asking about whether the official making the statement is trying to block access to the channel. And that's what these cases are about.
Finally, in the US, an official acting as such has very limited scope to suppress any expression, regardless of who might consider it "hate speech". SCOTUS has (unfortunately) given the FCC considerable leeway in constraining expression in certain media in certain circumstances,1 but that doesn't apply to social media.
In short: No.
On the other hand, nothing prevents Facebook or other soc-med companies from blocking or removing anything they (don't) want. Freedom of the press is for those who own the presses. They're not obliged to reproduce anyone's expression.
1Based on a medieval dread of communications which can "penetrate walls". Seriously, that decision was just short of calling radio witchcraft. A pathetic display of the fear of change.