There are cases where the First Amendment can apply to "private-owned public spaces", such as company towns [0] or shopping malls [1]. While such a designation has not yet been applied to Facebook, some are exploring the possibility of doing so [2].

[0] https://en.wikipedia.org/wiki/Marsh_v._Alabama

[1] https://firstamendmentcoalition.org/2010/08/free-speech-cali...

[2] https://www.bloomberg.com/news/features/2017-11-29/how-to-ta...