Public or private...if other hunters have the same rights I do on a particular track of land, then I will hunt anywhere I want or think they are not, with plenty of distance. If they move in on me, I'd ask them to back off....if they didn't, I have enough confidence to find a spot even better. I'm not going to waist my stand time next to a jackass who I believe is not as good of a hunter as me.
If someone marks something before me I would never or hangs a stand before I ever showed any interest or evidence of wanting to hunt the area, I would not hunt it. But that is me...
The fact of the matter is, their are always those pricks out there who don't give a flying !$#@ about anyone else. Just make sure when they're dragging one out that you show them the same respect when they ask for help...and make sure to invite your buddy with the military green uniform and the shiney badge to join you at his vehicle while you wait for him to drag it out alone.