I suspect information exchange and debating, was not meant to be enforced on private property during the constitution's writing. If I owned a tavern, I do not suspect the founding father's intent was for me to allow whatever kind of debate/information exchange to take place in my establishment. If anything, I suspect the opposite to be true.

If I own a coffeeshop today, I would have the right to restrict what is hung on my walls (e.g. advertisements, local events), and what is announced (i.e. someone loudly giving an announcement) to my patrons. I may not be able to control small group conversation though.

That being said, posting something publicly to Facebook is greatly different than DMing a person / group of friends. If Facebook deleted the image sent from one friend to the other, this would be a different conversation. I think your analogy and inspection of the constitution's intent, even further justifies that Facebook has right to do what they did.