My run is topped with bird netting and it has been working fine. I think making the walls from it is also totally fine as long as you know (which you do) that it would be like cutting butter with a hot knife for any land based predator to rip or chew thru it. Birds of prey would not be an issue since they dive bomb and don't take the time to sit there chewing on it or tearing it apart with their "hands".
I discovered Deer Barrier when looking to put up an inexpensive barrier to keep out deer from my vegetable garden. It is light weight, somewhat invisible, and very inexpensive. You can get 7ft x 100 ft for $17. Some may call this bird netting, but the bird netting I am familiar with, birds can get tangled in. We have a lot of wild birds and my chickens sometimes forget about the deer netting and run into it, they just bounce. So we used cedar limbs, stakes and light weight rope at corners. to build a large run around the two coops we have. To prevent hawk entry, you would have to extend netting to cover the top., which I have seen done. Anyway we put up a chicken run about 75 ft long x 25 ft wide in an hour and a half.
When we put this deer barrier up we did it to keep our hens from wandering to the "wild" side of the yard. We live on 6 acres and about 4 of the acres are wild with foxes, skunks, possums, armadillos, raccoons, and who knows what else live over there. We have fencing, but it will not keep tree climbing predators out. We lost 2 chickens and a rooster, to we presume foxes during the day when they were free ranging. The rooster had followed his hen to the "wild" side of the fence when he was taken. The other was taken up a tree and over chicken wire when she was still a pullet, the 3rd was taken because she ventured too close to the wild side, was in the brush so the fox could get in and get out without being seen. They do not like to venture out into the open in the daylight when they sense people or dogs around, but she made herself an overwhelming temptation. So we created a run on the other side of our "Fort Knox" chicken area, in the safer part of our yard to protect them from themselves. We also, re-homed our the 3 surviving members of our flock that insisted on escaping to the "Wild side" and began a new flock with breeds that have bit less wanderlust. So far so good. Our two grown chickens, a Barred rock and an Australorp hang out with us on the deck or hide under the deck, or are never far away from us our dogs, the house or their house when they are out free ranging. And the Australorp was still a very young hen when our bantam Cochin was taken, and she was traumatized by the event.If she ever detects anything that she feels may be foe she flies, climbs up to the highest part of our largest oak trees and squawks the alarm until we come running.
I am realistic to know that there may be a time when everything fails and someone gets eaten again, the downside of being on their place of the food chain, but we have tried to do everything we can to safeguard them. But I am not willing to take away their freedom entirely. They need to forage and roam, despite the hazard. Nothing in life is guaranteed. Our new flock consists of a standard Cochin Rooster, a Cochin hen, two Orpingtons and two Australorps. We picked this mix hoping to have enough "home bodies" like our other two. They are still pullets, they have a couple more months before they begin laying, and until then we keep them in the deer barrier run when we are home and when were not they go into Fort Knox: