If you read the ruling, it's not a crazy stretch.
"The more an owner, for his advantage, opens up his property for use by the public in general, the more do his rights become circumscribed by the statutory and constitutional rights of those who use it. Cf. Republic Aviation Corp. v. N.L.R.B., 324 U.S. 793, 65 S.Ct. 982, 985, 987, note 8, 157 A.L.R. 1081. Thus, the owners of privately held bridges, ferries, turnpikes and railroads may not operate them as freely as a farmer does his farm. Since these facilities are built and operated primarily to benefit the public and since their operation is essentially a public function, it is subject to state regulation."
The argument here would be that Facebook is built and operated primarily as a benefit to the public (i.e. they draw income by being a benefit to the public), they are essentially a public function, and are subject to state regulation as such.
Facebook would remain privately-held, and could either remain open to the public and subject to constitutional scrutiny, or they could close off and become some kind of a private club like Clubhouse.
I haven't thought through the ramifications of doing so, but I think it could be legally supported.