Under normal circumstances the whole concept of govt property somehow being like private property would be laughed out of court, and society as a whole. But nowadays everything seems open to interpretation and "common sense" (as in "common sense dictates that parks should be a safe place and therefore free of firearms).
So, I'd say yes - if we continue sliding down this slope, all bets are off. I'm sure that "right wing extremists" would have a tough time gathering in public places if all of a sudden the public places were recast as equivalent to private property in the context of govt controlling lawful activities authorized to take place on such property.
George Orwell would be proud.