After the events of the past couple weeks I felt I would weigh in with a bit of natural science. This being learned by living on a farm, something the PETA panderers apparently never did.
My first point is this:
Their main argument seems to center around two species, one of them invasive to the region. The desert tortoise, and wild horses. Guess which one is the invasive species... Some have argued that horses are here naturally, they are not. The horses of today share a common ancestry from Asia, the Middle East and other parts of the Mediterranean region. The horses of Ancient America migrated to these other lands over the Bering Land Bridge or died off. Only to be reintroduced to the Americas by the Spanish. Which is why we still refer to the wild horses of the west as Spanish Mustangs, whether they have much in common with the old Spanish herds or not.
Now for my second point:
My family has raised both cattle and horses on the same land. Now I'd like to point out this is in southern Missouri not the arid climes of the Southwest. As always I could be wrong depending on the location, but here it is anyway. I'd like to say, coming from my actual experience. Cattle are incapable of overgrazing land ahead of horses. Horses by nature of their articulating lips can draw graze into their teeth and are far more dangerous to future growth than cattle. We've grazed horses on ground that was eaten down by cattle to the point that they (the cattle) could no longer forage enough to continue on it and had to be moved to another pasture. Just ahead of us turning the horses into the former pasture to graze what the cattle couldn't for several weeks to a few months depending on time of year and rainfall. YMMV.
As for the tortoise, by the nature of natural selection of turtles and tortoise, they tend to outlive humans, cattle, horses and government agents (who I have doubts about being human), some have even outlived entire governments. While not the same species there is something to be said for living your life slowly. You don't have to fight your competitors if you can outlast them, and their great-great-great-grandchildren.