Z there is no "right to protest" on someone else's property.  I can't come in your home and start demanding you use less plastic.  I can't stand in your driveway and prevent you from parking or entering your home.  If you're building a shed in the back, I can't go in your backyard and physically block the way to prevent you from building it.  That's not a "right" that is protected by the US constitution.  

In the same way that you would probably call the police if I were standing in front of your doorway in your home and preventing you from entering, the police are there to remove protesters who are unlawfully using another person's private property.  It doesn't belong to them.  So no, they actually DON'T have a "right" to "protest" on another person's private property.  That never was nor ever will be a right guaranteed by the US Constitution.  I can't just set up shop in your backyard and start sign waving for Kelii Akina.  It doesn't work like that.  That's not my "right."