If current trends continue, all of humanity will become displaced people in another few hundred years. Displaced from the natural world, living in some kind of mostly artificial system mostly alien from anything a person of the 20th century would find familiar. This is progress? Perhaps. But there is value in the natural world that should not be thrown away just so humans can occupy twice as much area.
O.K., fine, but how do we get there from where we are today? Well, in simple terms, people who live or own interests in areas designated as preserves would be compensated and relocate to non-preserve areas of their choosing. During the decades while exact boundaries of preserve areas are determined, actual full exclusion would still be more than a century away, with a lifetime to apply their compensation to acquisition of land or a place to live in the developed areas for them and their children. A gradual phasing in of exclusion might include a progression such as: no new road construction after T-50 years, no new building construction after T-40, no immigration into preserve areas after T-30, no sale of leaseholds or other real property after T-20, limitation of fuel import and vehicular traffic after T-10, cutting electric power distribution at T-5, cutting wired communications at T-2, removal of all metal tools and implements at T-1, etc. Persons who wish to pursue an indigenous lifestyle in the preserve areas are a whole other topic onto itself, but after preservation is established, no non-indigenous human use of the preserve areas will be permitted, enforcement by removal of violators and exclusion from entry.
Do we build walls? Walls and other physical barriers actually worked fairly well for the U.S.S.R. for almost 30 years. Shoot to kill would seem to be a more extreme policy than we would need today, or in 2150, more like interdiction of violators on their return to the developed side. What is restricted is entry to the preserve areas, but what is mostly enforced is return to the developed areas. There may be some need to enter into the preserve areas to dismantle and disrupt forbidden activities, but for the most part, enforcement can concentrate on keeping the border from being violated. On the open seas, satellite tracking should prove efficient for enforcement of the “No Fishing, No Trespassing” zones, perhaps augmented by aerial surveillance in near-shore areas where smaller boats might evade satellite detection. All this sounds like a horrid restriction of freedom, and it is, but letting mankind run freely across all the land has not had a beneficial effect on the environment in the fertile crescent, and we are rapidly doing the same thing to most areas on Earth that are of any value to people.
In short: displacement for half is preferable to suffocation for all.