In United States a private business is free to shut down any speech it likes on its infrastructure/premises*. If you look closely, you will find that most or all do it to some speech or other. The revealing part is specifically what speech gets shut down.

In other words, unless you believe Facebook is part of State or acts on behalf of the State, “you don’t get to shut down hate speech” is mereley your sentiment, not something Constitution requires from them.

If Mark Z actually called hate speech “protected speech”, it is something he is free to do, but Facebook is also completely free to suppress hate speech.

* https://www.nyclu.org/commentary/column-applying-constitutio...