It's agriculture that isn't sustainable, not the ranching of livestock.
Agriculture is based on annual monocrops. A tilled field is a virtual wasteland because the farmer uses herbicides and pesticides to kill (nearly) every damn thing in the field except his crop, including the bacteria. The very turning of the earth causes the loss of topsoil and the plants themselves leech minerals and nutrients from the earth. So not only do you have to artificially replenish the soil, it takes considerable energy in the form of fossil fuels every growing season to plant and to harvest the crop.
Before 1950, agriculture ran on sunshine. Since then it has run on the Haber-Bosh process nitrogen fertilizer, and the Haber-Bosch process runs on fossil fuels. World-wide fertilizer use increased by >600% between 1961 and 1996 and between 1963 and 1997, world crop production doubled. There already would have been widespread famine without the Haber-Bosch process to support the planet's 7.8 billion people. It's as much as edible energy.
From Daniel Hillel's
Out of the Earth: Civilization and the Life of the Soil:
... and this ...
And from Richard Manning's
Against the Grain, How Agriculture Has Hijacked Civilization:
After clean water, the single resource that is second most limiting to the scale of human occupancy of the planet is phosphorus. We have to replace the phosphorus that agriculture removes from the earth. And what is the predominant source of agricultural phosphorus?
Ground bone meal of land animals, which comes primarily from abattoirs and slaughterhouses.
A pasture is a generally hospitable environment and all are welcome that pose no threat or competition to the livestock. Cows, sheep, and goats shit fertilizer and the action of their hooves serves to stabilize the topsoil. The traditional meat-producing livestock all leave the pasture a better place than they found it. Which is why grazing pasture is indispensable to any economically sensible crop rotation plan.
MMGW is a myth but even if it weren't the problem with cow farts is that termites produce even more methane than cows. So there's not much point fretting over cow gas until you've dealt with the termite problem.
The most favorable comparison I've seen of organic practices concluded it's 20% less productive than conventional farming. All the others were substantially less favorable than that so if you're concerned about sustaining our continuing population explosion, you need to ban organic farming, not cattle ranching.