They're not policing what you share with your friends, just what you can do on their platform. They are under no obligation to provide infinite reach for whatever drivel you want to share.
If you're sitting in a bar sharing racist anecdotes with your friends, that bar has the right to kick you out if they feel like. It's their bar.
If you don't like what Facebook's policies, go share somewhere else. There's even an alt-right social network you'll fit right in on.
> The problem is that they are not open. My only problem is opacity.
They're completely open about it. They've posted multiple stories about how they're addressing this, will provide links to third-party analysis for any flagged stories, and list the criteria for third-party fact-checking. [0]
> Moreover they coordinate with politics, so this has everything to do with the Bill of Rights at this point.
No, it does not. The Bill of Rights restrains what the government can do, it has nothing to do with what individual corporations can do.
Do you also think Smith & Wesson should be required to provide free guns, since the right to bear arms is in the constitution?
[0] http://www.poynter.org/fact-checkers-code-of-principles/