That's more a matter of scale, I think, than material? Whether it's wool or leather or plastic or cotton or hemp or flax, if you need millions or billions of units of something, it's going to incur large scale habitat loss somewhere in the world.
I guess then it's a question of land use (converting ecosystems into rangeland) vs pollution (from fossil fuels and plastics).
Well, wool is particularly bad, emitting way more greenhouse gases than most other textiles for equivalent fabric output. And sheep farming has quite a shocking impact on biodiversity.
Vox cites a LCA database but not a particular study or metastudy. I tried to look for it but couldn't find the exact one.
It seems to me like the kind of thing where the numbers could be drastically different depending on where you draw the boundaries (for plastics, does oil extraction and refining count?) and the sorts of impacts you consider (not just CO2E but as you mentioned, biodiversity, water, waste stream, etc.).
I'm inclined to believe the overall point of that post (sheep make a lot of methane, as any ruminant). But I'm not sure that banning wool outright would have the desirable outcome. I don't think cotton can replace wool in many situations, especially in wet outdoor environments. Would replacing it with (new) synthetics, which is the most common substitute, really be a net positive across all the impacts?
Edit: I don’t think cotton is the best replacement. I’m no expert, but I think hemp, flax, and tencel are the “best” replacements in terms of sustainability.
Cotton is a terrible replacement for cold/wet. Not sure any of those other are great though. Don't know much about tencel but the manufacturer's advertising certainly doesn't frame it as a cold/wet clothing material.
I guess then it's a question of land use (converting ecosystems into rangeland) vs pollution (from fossil fuels and plastics).