If Facebook wants to own the public forum they have to manage it as well.

Their power comes with responsibilities to keep it lawsful for all participants. That means removing unlawful speech while at the same time allowing lawful speech.

It's only logical that conflicts needs to be settled in a similar fashion as they are in other similar situations in the offline world.

For western democracies that usually means some sort of due process and unbiased weighing of facts with a decision that adheres to the existing standards in that society.

Facebook would like to do everything automatically of course but with great power comes great responsibility.

I predict that sooner or later the regular court system will be responsible for those cases and Facebook will be happy to make money by providing the tech platform.